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In the Grip...

The book In the Grip of the Distant Universe] by Neal Graneau should be a good source for representing David's viewpoint that the typical way modern physics deal with inertia and centrifugal force using "fictitious" forces is a travesty. I don't happen to agree with that assessment, but there is a good reasoned argument here for a point of view based on Mach's principle, which I like. The author thinks the way it's taught now is "shameful", but it also seems clear that he just doesn't accept the the term "fictitious", saying "Presumably, this means they do not really exist." This is the same nonsense that David pulls -- instead of looking at what fictitious means, he makes up a strawman interpretation to criticize. Anyway, it's a source, so if we attribute such a POV to that author, it should be fine. Dicklyon (talk) 01:40, 17 May 2009 (UTC)

Dick, I never tried too hard to figure out what the word 'fictitious' means in the context of centrifugal force. The word is misleading at the best. As far as I am concerned, centrifugal force is a radial force without the need for any further qualifying adjectives. I've just looked at the reference which you have provided and I can see that this guy Neal Graneau has got his head totally screwed on. He is saying the exact same as what I have been saying all along. David Tombe (talk) 01:04, 18 May 2009 (UTC)

Ironically, fictitious forces are characterised by not obeying Newton's third law.

Tell me again, does centrifugal force in your polar coordinate equation obey the third law or not?- (User) Wolfkeeper (Talk) 21:52, 27 May 2009 (UTC)

So, I've been reading this book while traveling. It's quite strange really, but also it turns out not at all like David's POV. The authors Graneau and Graneau are seeking to explain the "ma" in F = ma as a "force" of inertia, pushing back in the opposite direction, such that there's a "dynamic equilibrium" in which all forces sum to zero, for any acceleration. It's exactly the "reaction force" or "Newton's thrid law" approach (they do say as much) plus a few different words to reinterpret F = ma, but its really mostly about trying to get at where this reaction force comes from, using Mach's principle, that it must be an interaction with all the distant matter in the universe, with instantaneous communication. I don't buy the argument that it has to instaneous, as others formulate similar theories with speed-of-light advanced and retarded wave functions, but that's not really relevant here. Want's interest though is the extent to which they don't understand, and vehemently criticize the other use of centrifugal force to describe a pseudo force in a rotating system. They don't realize that these different conceptions are in no way in conflict with each other, they're just using the same term for different concepts. It's really quite bizaree that they would right a book displaying such strong feelings about a simple misunderstanding.

As to the Leibniz approach, I suppose that if you took the r-double-dot in the co-rotating 1D or 2D system, and converting it to a corresponding inertial force and put it on the force side, there would still also be a centrifugal force term that in combination with it would make a total inertial force equal to the gravitational force; yes, that would work. Then the sum of accelerating forces balances the applied gravitational force, so it's just Newton's third law stuff again, resolved into two parts. But that's a stretch, as they don't go near anything that looks like the Leibniz approach. Dicklyon (talk) 20:19, 24 May 2009 (UTC)

Putting the edit war behind us

I think this article is on the right track, but what will ultimately drive consensus and produce a good article is if everyone plays by the rules, specifically: 1. Report but do not promote (or refute) a particular point of view expressed in the sources (WP:NPOV and WP:SOAP); 2. Explain what is known about CF without instructing the reader (WP:NOTTEXTBOOK); 3. Always assume good faith in others' edits and assume the other editors are intelligent, well-intended people with a valid misunderstanding (WP:AGF and WP:CIVIL); 4. Always take discussion to the talk page BEFORE reverting an edit (unless it has already been thoroughly discussed - then be sure to indicate that discussion in your edit summary); 5. Stick close to the sources and avoid synthesis (WP:Verifiability, WP:RS, WP:SYNTHESIS); 6. Provide ample in-line citations for maximum clarity and verifiability (WP:Verifiability, WP:CITE); 7. Always be sure to identify the common ground where you do agree with the editor(s) with whom you find yourself in disagreement, and spread a little wikilove to those who have done something innovative or commendable, even if you often disagree with the same editor ("Love thy enemies...", what better way to bring someone out of their shell?). If you have held a long-standing disagreement with an editor about one thing, and they do something else which you agree with, leave them a pleasant note about it on their talk page. It will mean a lot to them and can help deescalate the disagreement. The whole thing boils down to this: show me an edit war and I will show you a group of editors that are ignoring the rules to pursue their own agendas. So when these things flare up, just keep cool and be specific and factual in your counterarguments, and cut a wide berth around any sort of personal attacks. We are all just editors, and our egos meaningless; our very raison d'etre is to produce a better article for the reader, and everything we do should serve that purpose. If we maintain this frame of reference, there is never any need to make personal attacks, nor to take any criticism personally. When personal attacks are made, they say much more about the attacker than the target. One might think a group of physicists would be particularly well-suited to the sort of objectivity and emotional detachment from the material that is required to produce a good article and avoid edit warring. In the end, of course, we are all people, and all our work is subject to all the flaws and vulnerabilities that go along with that. I'll keep this article on my watchlist and try to help out with it from time to time, but I think we have the basis of a good article here already (in what must be some kind of record time). Thank you all for helping to put the edit war behind us. It took all of you to make this progress, so my thanks go out to each and every one. Wilhelm_meis (talk) 04:01, 17 May 2009 (UTC)

Wilhelm, thanks for your intervention. It took the intervention of a neutral arbitrator to break the deadlock. I think that it would now be beneficial to actually try and analyze the cause of the edit war. Had it simply been an open clash of differing opinions on the topic, with everybody openly admitting their prejudices, then I'm sure a compromise could have been found a long time ago. But unfortunately that was not the nature of the edit war. The edit war began because a certain group did not want to believe that there could possibly exist other opinions on the topic beyond that which had formed a part of their education.

Unfortunately, at the beginning, I wasn't very persuasive and I didn't have any sources immediately at hand. But by the time I started to introduce sources, the opposition were so dug in and re-inforced that it simply became a childish game of sniping from behind screens. It all came down to the issue of superior numbers.

While Dick doesn't appear to favour my point of view, at least he was honest enough to present to me with the historical origins of my point of view, which I had previously been unaware of. We have all learned alot from this edit war. I hope that the last stage is done more maturely and in such a way that we can all learn more about the topic in the process. I think that we should all openly declare our prejudices on the topic. My future contributions will now be to highlight the historical sources of the differing and changing attitudes to the topic. David Tombe (talk) 11:14, 17 May 2009 (UTC)

No one gets to point fingers here. As they say, it takes two to tango. If the minority opinion had been squashed altogether, there would not have been much of an edit war. Of course that doesn't mean it would be a better article - it would have NPOV problems and lacunae in its coverage of the topic, but not much of an edit war. If you really want to get to the cause of the edit war, it wasn't that people were dishonest about their opinions or that anyone was obfuscating their motives; it's that people were too emotionally invested in the material. They weren't just reporting what was said by whom in what source, they were defending their own views. This was an edit war on par with those in the histories of articles on abortion and evolution, because people were approaching it in the same way. It all comes down to this: dispassionate objectivity is the key to maintaining neutrality, and without it edit wars are inevitable. We cannot write our own dearly held views into the articles we edit. Remember, this is an encyclopedia, not a textbook. You don't get to write whatever you want here. We report on what is written in the most reliable sources available. That's what an encyclopedia is. And that's where these articles fell short for so long. People forgot they were editing an encyclopedia and thought they were writing a textbook. People were defending their own views, rather than reporting the views of the experts. No one here is an expert, we are just editors, and we would all do well to remember that. That is what caused this edit war, and it is the very same thing that has caused a good many other edit wars elsewhere on WP. Everyone involved in any edit war shares in it, not just the person making "tendentious" edits, and not just the people "trying to squash" the minority opinion. We're all in the same mud here, and if we're to get out of it, it will be together. Wilhelm_meis (talk) 02:29, 18 May 2009 (UTC)

The problem is that David spent a year arguing without sources, except for one where his interpretion was pretty much contradicted in the source, and aliening everyone who tried to reason with him. But since I found him some sources, we're making progress. Dicklyon (talk) 04:32, 18 May 2009 (UTC)

Dick, I appreciate your honesty in bringing forth sources that have backed up my opinion. It makes it easier for me to reciprocate the gesture by acknowledging that the opposition viewpoint dominates the modern textbooks. On that basis, we can move forward. We can put the opposition viewpoint first place in the article and state that it is the most common approach nowadays. But we will also now have room to describe the Leibniz approach further down and mention the muted manner in which it is dealt with by Goldstein, along with some modern efforts to treat the planetary orbital problem within the context of rotating frames of reference. But we cannot suppress the fact that 29 years ago, I did planetary orbital theory without involving rotating frames of reference, and that I saw many different approaches to planetary orbital theory which didn't use rotating frames of reference. And those texbooks are still floating about in the stacks somewhere.

On that point I call into question the line in the introduction (The Roche reference) which talks about two distinct but equally valid approaches to centrifugal force. I don't know what he has in mind for those two approaches. But if he is talking about the rotating frames approach and the Newtonian approach then that sentence needs to be removed, because it effectively denies the existence of a third approach. This is were the issue of references can become tricky unless discrepancies can be brushed over in a mature fashion. If we have references that show that there are three approaches, and then we have a reference which states the opinion of a man that there are only two approaches, we cannot allow that latter reference to dominate the article. We need to talk broadly about the several approaches. That is why I inserted the line about 'several approaches'. An anonymous from Norway removed my line. Despite a large number of edits by Brews, this anonymous honed in and deleted my edit in particular. I'm very glad that you stepped in and reverted it. But we now need to remove the clause which narrows it down to 'two approaches'. The truth is that there are at least three approaches to this topic. Besides, it is quite ridiculous to state that there are two approaches that are different but both equally valid. If the two approaches are different, then they cannot both be equally valid. One of them must be wrong, and so we shouldn't be making statements such as to paper over cracks, even if it is the quote from some man who wrote a textbook in 1991. Do you agree with me that the Roche reference should be taken out as a beginning for a slightly expanded introduction? David Tombe (talk) 12:40, 18 May 2009 (UTC)

David, the two approaches can indeed be equally valid; they are just different definitions of what centrifugal force is. The Liebniz approach is problematic, as a third approach, as it doesn't connect to F=ma as we know it. I still think you are mistaken to say that Goldstein used that approach, or that you did planetary orbits without rotating frames of reference. If you work out the accelerations in polar coordinates, under the force of gravity, th term you care about appears on the acceleration side as a centripetal acceleration. Only by taking r-double-dot as an acceleration can you interpret that term as a centrifugal force. The only frame in which r-double-dot is a acceleration is the one that co-rotates with the planet. So by doing the algebra, without knowing it, you moved to a co-rotating frame. This is consistent with one of the two definitions of centrifugal force (not the reaction force, but the fictitious force, where fictitious means it's zero in a special non-rotating frame). So, while you have a different "approach", it's the same definitioin and results, and a special application of, the usual dominant method. I agree that Liebniz and Graneau don't conceptualize it this way; Liebniz because he didn't understand F = ma yet, and Graneaux because he has an axe to grind, like you. So you need to find a way to report this stuff without saying there's a third way, I think; the history of conceptions section is the place. Dicklyon (talk) 14:41, 18 May 2009 (UTC)

Dick, the facts are that there are three approaches, and that only one of them can be correct. The planetary orbital equation is a central force equation. All forces in that equation are radial forces. There is an inward inverse square law force of gravity and an outward inverse cube law centrifugal force. The equation can be found at 3-12 in Goldstein without any mention of rotating frames of reference. The Leibniz equation, which is the same as equation 3-12 in Goldstein covers for every possible scenario which you could possibly encounter involving centrifugal force. The Newtonian approach is wrong because it restricts centrifugal force to being equal and opposite to centripetal force, and the rotating frames approach involves an unnecessary encumbrance which becomes completely wrong when it allows the Coriolis force to swing into the radial direction.

Let's sort that latter business out once and for all. Equation 3-12 tells us that in the special case of circular motion, the centrifugal force must be equal and opposite to the centripetal force. In the rotating frames scenario in which a stationary object is observed to trace out a circle as when observed from a rotating frame, I would say that there is no centrifugal force acting at all. You say that there is, but that it it counteracted by a centripetal force that is twice as large and which is supplied from the Coriolis force. Well if the centripetal force is twice as large as the centrifugal force, then we cannot have a circular motion under the terms of equation 3-12. David Tombe (talk) 15:25, 18 May 2009 (UTC)

In general the centrifugal and centripetal are not equal and opposite in Newtonian mechanics, that's only true for circular orbits. Newton thought that they must be equal for a while, but that's all; at the end of the the day he knew perfectly well that that doesn't hold for elliptical orbits.- (User) Wolfkeeper (Talk) 14:24, 19 May 2009 (UTC)

Wolfkeeper, You are misrepresenting what I said. I said that centripetal force and centrifugal force are not in general equal and opposite. They are only equal and opposite in the special case of circular motion. Hence in the scenario where you guys try to justify centrifugal force on non-rotating objects by using an oppositely acting Coriolis force to act as the centripetal force, you have got it all wrong, because you are claiming to have an apparent circular motion in which the centripetal force is twice as large as the centrifugal force. David Tombe (talk) 11:43, 20 May 2009 (UTC)

If I may butt in for a minute, as I recall the "two approaches" referred to 1) Physics and 2) Engineering, but then someone objected to the Physics v. Engineering dichotomy (see above discussion). I don't think the original edit was in reference to Newton v. Rotating Frames at all. Wilhelm_meis (talk) 02:23, 21 May 2009 (UTC)

I objected, since I know the fictitious force approach is widely used in engineering, e.g. in robotics, where the joint torques needed depend on whether the member carrying the joint is rotating due to a previous joint; if some author draws this dichotomy, it's OK to attribute that idea, but it's by no means universally viewed that way. Dicklyon (talk) 03:22, 21 May 2009 (UTC)

The bottom line is that it's wrong to make an unequivocal statement in the introduction to the extent that there are specifically two approaches to centrifugal force when in fact the literature points to at least three approaches. The problem would be solved by removing that sentence altogther as it is not necessary. It is only misleading. David Tombe (talk) 09:45, 21 May 2009 (UTC)

Tombe revisions

Hi David:

I disagree with almost all your recent changes on this page.

One issue is the prominence given to what you call Leibniz position, which prominence is not justified based upon the present day view of matters, as you have frequently complained. The present article as you have re-written it does not adequately warn the reader.

Your view of centrifugal force also is very tightly tied to the problem of planetary motion, which is only one very specific problem, and one tightly admixed with gravitational attraction. That specific example is not a paradigm for all of centrifugal force.

I vote to revert all your recent edits. As proposed by someone earlier, these Leibniz opinions should be in the history section. The table should be restored to its original form, with all the rows and no Leibniz column. Brews ohare (talk) 12:24, 19 May 2009 (UTC)

Brews, I didn't give any prominence to the Leibniz position. I added it as an alternative position alongside the other two positions. You on the other hand appear to want to consign it to history even though it appears in Goldstein's 'Classical mechanics'. David Tombe (talk) 12:23, 20 May 2009 (UTC)

I've reverted the massive undue weight. Leibniz was never able to come up with a consistent theory; he thought the planets were pushed around by a solar vortex around the Sun, but if that was so, the radial motion you need for elliptical orbits would have damped right out; ultimately his theory doesn't work.- (User) Wolfkeeper (Talk) 14:27, 19 May 2009 (UTC)

Wolfkeeper, I certainly don't support a solar vortex concept. I oppose Descartes on the grounds that one large vortex would consign all orbits to the same direction. But that doesn't really matter too much here. The point is that Leibniz produced the radial planetary orbital equation as it still stands in modern textbooks. It doesn't matter what Leibniz thought the physical explanation is. David Tombe (talk) 12:27, 20 May 2009 (UTC)

Here's the strange table per David, so we can discuss it here (my line breaks added): Dicklyon (talk) 00:16, 20 May 2009 (UTC)

The table below compares various facets of the concepts of centrifugal force.

So, David, I have to ask for some clarification of your thinking. If the Leibniz method works in "any" reference frame, what is meant by the "rotation axis"? And where it says "induced by absolute rotation", rotation of what? Didn't you already agree that it depends on the viewpoint? Isn't it rotation about a chosen viewpoint, giving rise to an acceleration in the r dimension that you're talking about? And does it, or does it not, give rise to a force that can be used in Newton's laws of motion? Dicklyon (talk) 00:19, 20 May 2009 (UTC)

Also, no basis laid in this article to understand the items in the table: for example, where did the inverse cube of radius come from? Answer: another article.

Also, this table uses Isaac Newton as a column heading as though Newton is associated only with the reactive form of centrifugal force, and doesn't explain that.

However, the main point is that we don't need to introduce Leibniz outside of the historical section.Brews ohare (talk) 01:47, 20 May 2009 (UTC)

Plus it's a gross mischaracterization. The Liebniz method, as far as we know, is only for the case of a radial aligned with the gravity vector; that is, it's not "any" frame, but only the frame centered at a center of a one-body problem and co-rotating with that body; at least, that's all that I've seen attributed to Leibniz, and is what Goldstein did. Dicklyon (talk) 02:25, 20 May 2009 (UTC)

Yes Dick, I realized that mistake later. That bit alone could have been changed. There was no need to delete all my edits because of it. The Leibniz equation is identical to equation 3-12 in Goldstein. The frame of reference involved is the inertial frame of reference. The angular velocity is measured relative to the inertial frame of reference. It is not a historical issue. This is a question of an inability of you guys to accomodate a perfectly legitimate approach to centrifugal force. Brews seems to think that the planetary orbital approach is only one facet of centrifugal force. It is in fact the most general approach which covers every case scenario. I am afraid that we are dealing with a situation here in which the article is being controlled by a group who do not fully comprehend this topic. Wolfkeeper was completely wrong in his assessment of the situation. The outward inverse cube law centrifugal force acts in tandem with the inward inverse square law force of gravity. The two power laws lead to stable equilibrium nodes and orbits which are hyperbolic, parabolic, or elliptical. That was Leibniz's approach and it is the approach which I learned at university and which appears in modern textbooks. You are insisting on restricting this article to the most common modern approach and placing it alongside a redundant Newtonian approach. You are falsifying the situation by promoting your own preferred point of view in conjunction with an acceptable face of opposition, and deliberately suppressing the third way.

And one final point. You were very quick to spot that error. That proves that deep down, you fully understand the issue. Why are you so keen to consign the radial planetary orbital equation, relative to the inertial frame, to the history books?David Tombe (talk) 11:36, 20 May 2009 (UTC)

That set of errors was not the reason for reverting your strange table. If you can provide a meaningful improvement to the table we have, or somehow manage to make a coherent interpretation of Liebniz's POV on CF (based on sources, that is), that might be interesting; but present it here first, instead of messing up the article with it. As far as any of us can tell, the Liebniz approach is still just a special case of the rotating frame approach, for the frame centered at the center of the one-body problem and co-rotating with that body. Check for example the Meli 1990 paper (ask me if you need a copy) where it says the Leibniz approach was "close" to Daniel Bernoulli's views; but the situation back then was very complicated, and essentially impossible to coherently relate to modern physics except via the concept of pseudo forces. Dicklyon (talk) 05:16, 21 May 2009 (UTC)

Dick, 'That set of errors'? There was one error. I should have written 'inertial frame' where I wrote 'any frame'. As regards a coherent interpretation of Leibniz's equation/equation 3-12 in Goldstein/problem 8-23 in Taylor, a coherent interpretation should not be difficult. The problem here is that you don't want it on the page at all, so you will argue that any attempt to describe it without involving rotating frames of reference is incoherent.

Leibniz's equation does not need to be interpreted in terms of rotating frames of reference. The fact that you can produce a few references that attempt to do so does not mean that it has to be done so. Goldstein does not use rotating frames of reference.

Your tactic here is to consign the Leibniz equation to the history section because it conflicts with the rotating frames approach. And you are using the specious argument that it is one and the same approach and hence doesn't need to be mentioned. All three approaches share a common element. The Leibniz approach shares a common element with the rotating frames approach and the Newtonian approach but that doesn't mean that it is the same approach. You are deliberately trying to suppress an approach which you don't like because it was not the approach that you were first taught.

I thought that you were interested in compromise here, but now it seems not. You are trying to falsify the picture by emphasizing that there are only two approaches to the topic. David Tombe (talk) 09:56, 21 May 2009 (UTC)

The errors are in not noting that it's only in a co-rotating frame, and not saying what's meant by "rotation axis", etc. Generally, it's not a good characterization. In an inertial frame, the accelerations are completely described by the real forces, with no need for the centrifugal force term, so it's not clear why you would claim inertial frame there. There are only two modern and consistent approaches that I'm aware of. The historical approaches were complex and inconsistent, as the cited refs make clear. From a modern perspective, the Leibniz approach is just the rotating frames approach, as Taylor's derivation, and Goldstein's, make clear. And it's not necessary to impute negative motives to my edits; I've been doing all I can to settle the edit wars around the polarized fights that you and the others carried on for over a year before I came here; I found you sources that you can use to correctly position the approach historically and technically; I can't help it if you can't get over your hangups. Dicklyon (talk) 17:23, 21 May 2009 (UTC)

Dick, Goldstein does not use rotating frames of reference for the planetary orbital equation at 3-12. You keep saying that he does. But he doesn't, and so you are deliberately trying to distort the facts. I never used rotating frames of reference when I did orbital mechanics. It doesn't matter that you happen to have found a few references involving attempts to strap a co-rotating frame around the Kepler problem. If the Kepler problem can be dealt with without using rotating frames of reference, then we do not need to use rotating frames of reference. Goldstein deals with equation 3-12 using plane polar coordinates with all displacements measured relative to the inertial frame. Absolute rotation induces an absolute outward expansion pressure. That is what centrifugal force is all about, and that is what you are trying to hide.

You have to ask yourself why you are trying to block such a simple exposure of the concept from appearing in the article. It is not original research and there is no problem as regards reliable sources. But you are determined to either subsume it into the fictitious rotating frames of reference approach, which it doesn't match in every respect, or to consign it to the history section.David Tombe (talk) 18:48, 21 May 2009 (UTC)

Goldstein's section "equivalent one-dimensional system" is where he converts the centripetal acceleration term in eq 3-12 to a centrifugal force term in 3-22, corresponding to a rotating 1D system along the radial. Any system in which r-double-dot is an acceleration is necessarily rotating. I don't understand what you're saying about eq. 3-12; absolute rotation of what? It's just F = ma in polar coordinates in an inertial frame; do you see centrifugal force in 3-12? The only term on the force side is f(r), which represents gravity. The acceleration side has a centripetal acceleration term. Goldstein's approach is standard; Liebniz's is historical; feel free to describe them both, correctly, based on what sources say about them. Dicklyon (talk) 23:06, 21 May 2009 (UTC)

Dick, you are hopelessly confused. There is no need to mention the equation for the 1-D problem. We are talking here about the 2-D problem at equation 3-12 in which the outward radial inverse cube law term is the centrifugal force. It's the same as Leibniz's equation. Centrifugal force is an outward inverse cube law force, providing that angular momentum is conserved. It's as simple as that. By not seeing this simplicity, and by blocking it from the article, you are not helping the readers. David Tombe (talk) 11:43, 22 May 2009 (UTC)

So the question comes down to what the literature calls the second term in equation 3-12? Well, Goldstein calls it the "centripetal acceleration term" on page 25 (or page 27 in the 3rd edition), which makes sense since the inverse cube term in 3-12 looks like a radially inward contribution to the acceleration side of the equation. He only calls it the centrifugal force after moving it over to the force side of the equation and after introducing the 1D problem. He also refers to it as the "reversed effective force" of the centripetal acceleration. --FyzixFighter (talk) 14:50, 22 May 2009 (UTC)

FyzixFighter, you are hopelessly confused. The inverse cube law term in equation 3-12 can be nothing other than the centrifugal force. Let's not play silly games with the endless confusion in the literature. David Tombe (talk) 18:53, 22 May 2009 (UTC)

From Goldstein, Ch 1 (pg 27 in the 3rd edition) using the same Lagrangian formalism he uses in chapter 3 to get equations 3-11 and 3-12:

The derivatives occurring in the r equation are

${\displaystyle {\frac {\partial T}{\partial r}}=mr{\dot {\theta }}^{2}}$,

${\displaystyle {\frac {\partial T}{\partial {\dot {r}}}}=m{\dot {r}}}$,

${\displaystyle {\frac {d}{dt}}\left({\frac {\partial T}{\partial {\dot {r}}}}\right)=m{\ddot {r}}}$

and the equation itself is

${\displaystyle m{\ddot {r}}-mr{\dot {\theta }}^{2}=F_{r}}$,

the second term being the centripetal acceleration term.

So if I'm confused, so is Goldstein. --FyzixFighter (talk) 21:17, 22 May 2009 (UTC)

FyzixFighter, go on ahead and ruin the article with your twisted use of confused references. The administrators are on your side. Goldstein was clearly wrong on this point. A force can never change its direction simply by being placed on the other side of an equation. That term is the centrifugal force. It couldn't possibly be the centripetal force. The centripetal force only takes on that mathematical form in the special case of circular motion. Centrifugal force will of course get a negative sign if we bring it across to the left hand side of the equation, but that doesn't make it into a centripetal force. And I know that you must know that fine well. You are thriving on the confusion which you can stir up by sifting through the literature to fish out the endless inconsistencies and errors which exist. I on the other hand was trying to bring a coherent order to the mess for the benefit of the readers. But the administrators want to do it your way.

Goldstein uses the term 'centrifugal force' for the inverse cube law term in 3-12, and that is all that is important. And it shouldn't even have to come down to what Goldstein says, because we all know that it has to be the centrifugal force. It is the exact same planetry orbital equation that Leibniz produced. And furthermore, you didn't revert that edit a few days ago for the good of the reader. You reverted it because it drew attention to the fact that all is not straightforward in the literature as regards centrifugal force. You are playing a silly game here in which the literature is gospel, despite the inconsistencies and errors which you are clearly aware of, and you are doing this deliberately to undermine my attempts to bring order and understanding to the subject. I'm very sorry that the administrators are totally incapable of seeing right through you. David Tombe (talk) 10:15, 23 May 2009 (UTC)

Absolute rotation induces an absolute outward expansion pressure

This statement by David seems to encapsulate his viewpoint. I guess one can think of rotation without specifying relative to what. A question arises though: who gets to decide how rapid the rotation is? Can we identify the stationary observer who actually has got the rotation correct? How is that done?

If we cannot do that, everybody has a legitimate view of how fast the rotation is, and not everyone will agree. So, by implication, not everyone will agree on the "absolute outward pressure", which then is not absolute.

Newton solved this problem: if your calculation using Newton's laws with the rate you observe works to describe all the observations while using zero "absolute outward pressure", then you are in a stationary frame. In other words, the absolute "outward expansion pressure" is identically zero.

How do you describe the situation, David? Brews ohare (talk) 00:37, 22 May 2009 (UTC)

Brews, You have indeed asked the ultimate relevant question. That is what the rotating bucket experiment is all about. It shows that centrifugal force is a real outward expansion pressure that is induced as a result of absolute rotation relative to one frame of reference in particular. That frame of reference is marked out by the background stars.

Those are the facts. But it seems that alot of the problem here is that people trained in relativity think that this is not fair because it gives special physical significance to one frame of reference in particular. My guess is that here lies the root of the entire edit war. These people are trying to put their own modern rationalization on something which doesn't fit with how they think that things should be. And so they are trying to suppress the simplicity of the topic. David Tombe (talk) 11:49, 22 May 2009 (UTC)

It would appear that Newton suggests that absolute rotation is wrt the fixed stars. However, if the observer is stationary wrt the fixed stars, Newton says there is zero absolute outward pressure. Establishing this point is specifically his objective with the bucket argument and with the rotating spheres. So, my conclusion is that you disagree with Newton about this, or interpret his objective in these two examples as something different? Brews ohare (talk) 12:21, 22 May 2009 (UTC)

Brews, on this issue, I totally agree with Newton. The frame of reference that is marked out by the background stars, possesses special properties which become manifest when rotation occurs relative to any arbitrarily chosen point in space, relative to the background stars. But that doesn't mean that I relate the stars themselves directly to the physical cause. That's another matter and I'd be going into original research. I noticed that you have been editing on the electric dipole page. You will have seen that the dipole field is an inverse cube law force field. Does that not give you a clue?

I do however disagree with Newton's attempt to denigrate Leibniz's equation. Clearly Leibniz beat Newton to it. Leibniz got both the inverse square law for gravity and the inverse cube law for centrifugal force. He put it all into one equation. He was ahead of Newton. Newton only got as far as the inverse square law for gravity. Newton sabotaged Leibniz's equation by mixing it all up with his own third law of action and reaction. Hence, Newton's reactive centrifugal force is wrong in principle, but it is good in practice for circular motion scenarios.David Tombe (talk) 13:15, 22 May 2009 (UTC)

David: Your reply is non-responsive. If the observer is stationary wrt the fixed stars, Newton says there is zero absolute outward pressure. Establishing this point is specifically his objective with the bucket argument and with the rotating spheres. So, my conclusion is that you disagree with Newton about this, or interpret his objective in these two examples as something different? Brews ohare (talk) 13:23, 22 May 2009 (UTC)

Brews, I don't get your point. If it's rotating realtive to the background stars, there will be an outward expansion pressure. If it's not rotating relative to the background stars, there won't be. I assume that Newton was saying this too. David Tombe (talk) 13:27, 22 May 2009 (UTC)

I don't think Newton agrees with you. For example, with the rotating spheres Newton's suggestion is that a string tension is required in the frame stationary wrt the fixed stars only to provide centripetal force. The centrifugal force is zero in this frame. Brews ohare (talk) 16:49, 22 May 2009 (UTC)

No Brews, The centrifugal force on an object, relative to a point, depends on that object's own transverse speed relative to the background stars. In your rotating spheres example, the centrifugal force comes from their own transverse speed relative to the inertial frame (marked out by the background stars). That transverse speed induces an outward expansion which pulls the string taut. The tension in the taut string then applies an inward centripetal force which makes the spheres move in circular motion. In the circular motion, the inward centripetal force is equal and opposite to the outward centrifugal force. David Tombe (talk) 18:59, 22 May 2009 (UTC)

David: In the frame stationary wrt the fixed stars, the taut string provides a centripetal force that provides the inward acceleration necessary to change the direction of the velocity so it remains tangent to the circle, so circular motion occurs. There is no balancing of two forces, as that leads to zero acceleration and therefore to straight-line motion. I have a feeling of deja vu here. Brews ohare (talk) 23:05, 22 May 2009 (UTC)

Brews, you are falling into the trap of ignoring the outward centrifugal force that exists relative to the chosen origin, even when the object is moving in a fly-by straight line prior to the application of any centripetal force. That is the bit that modern physics teachers have overlooked. But it is not overlooked in the planetary orbital equation. According to the radial planetary orbital equation (Leibniz, or 3-12 in Goldstein, or problem 8-23 in Taylor), when circular motion occurs, r double dot will be zero, and the inward centripetal force will be exactly balanced by an outward inverse cube law centrifugal force. If there is no centripetal force, the centrifugal force alone will cause a hyperbolic orbit of infinite eccentricity, which is a straight line fly-by motion.

I have discussed this on forums. Alot of people can't see where the outward pressure actually lies in a fly-by straight line motion. But mathematically speaking, the centrifugal force is nevertheless there. It is built into the geometry of space. You can see it better if you extrapolate the situation to a four-body problem involving two adjacent two body orbits. If we criss-cross centrifugal force over any pair within the four, the two orbits will repel each other. That is how Maxwell explained magnetic repulsion. David Tombe (talk) 10:27, 23 May 2009 (UTC)

David: I despair of reaching any common ground with you as long as you stick to the planetary problem. I suggest that the focus be changed to the case of two identical spheres tied by a cord, and get the connection to gravity and Kepler's laws out of the picture. That puts things in a clearer context without unnecessary side issues. Within the rotating spheres problem, I agree with the presentations at rotating spheres. Maybe you would like to discuss centrifugal force in that case? Brews ohare (talk) 17:26, 23 May 2009 (UTC)

Brews, Planetary orbital theory is not a side issue. The equation,

${\displaystyle {\ddot {r}}=centripetalforce+l^{2}/r^{3}}$

or,

${\displaystyle {\ddot {r}}=centripetalforce+centrifugalforce}$

covers for any scenario in this topic that you could possibly imagine. When the centripetal force is gravity, it becomes Leibniz's equation. So let's look at your rotating spheres. Let's start with the situation before the string is attached. If we ignore gravity, the two spheres will move with a mutual transverse speed and they will both move in a straight line. This is the infinitely eccentric hyperbolic fly-by solution to the equation above, which arises when the centripetal force is zero. The line joining the two will be rotating, and there will be an outward centrifugal force acting along that line which is proportional to the inverse cube of the distance between the two spheres.

If we then attach a string, the centrifugal force will pull the string taut. The tension in the taut string will then cause an inward centripetal force to act. We will then have a circular motion scenario in which the outward centrifugal force is exactly balanced by an inward centripetal force, and as such ${\displaystyle {\ddot {r}}}$ will be equal to zero.

Remember this golden rule,

(1) Rotation causes centrifugal force

(2) Centripetal force causes curved path motion

and you will not go wrong. David Tombe (talk) 18:39, 23 May 2009 (UTC)

The equation l^2/r^3 is not physically different from rw^2, you just substitute l=r^2 w into the equation and you get the same thing. It's only trivially different.- (User) Wolfkeeper (Talk) 00:29, 24 May 2009 (UTC)

Wolfkeeper, You are absolutely correct, and I was fully aware of that fact. Do remember however that the inverse cube law form only holds in the special case when angular momentum is conserved. If you are genuinely interested in this topic, then there is hope that we might be able to make progress. Your edit above tells me that you have just realized something which I have been trying to draw your attention to for a long time. David Tombe (talk) 12:45, 24 May 2009 (UTC)

David: Your equations are tied to polar coordinates, and more than that, to a specific terminology attached to each term. That terminology prejudges the issues. To clarify what the forces and vectors are, one way is to leave polar coordinates and return to a formulation in a coordinate-independent language using vector calculus. In such language, dr / dt is acceleration. This acceleration in uniform circular motion is supplied by a vector force applied to the body due to the tension in the string all by itself, and no centrifugal force vector appears in the equations. On the other hand, in polar coordinates, translation of dr / dt introduces not only the dr / dt term, but another term you call the centrifugal force, but which is an artifact of the coordinate choice. Clearly, the translation of dr / dt into the language of a particular coordinate system does not reflect the nature of the problem being solved or the physical forces at work in a particular problem; rather it is a translation to the chosen coordinate system that is independent of the physical problem and dependent on the choice of coordinates. If you chose instead parabolic coordinates, this extra term would be different, again reflecting that it originates in the choice of coordinates, not in the forces at play. Brews ohare (talk) 20:52, 23 May 2009 (UTC)

Brews, we can express the equation in plane English without using any mathematical symbolism at all. The physics is not dependent on the language that is used to describe it. The single equation which applies to any scenario which you could possibly present me with in this topic is,

Radial Force = Centripetal Force + Centrifugal force

You give me any scenario that you like and I will analyze it for you in terms of this equation. Leibniz's equation is simply a more mathematically detailed version of this equation which specifically uses the inverse square law of gravity for the centripetal force along with the inverse cube law version of centrifugal force, since angular momentum is conserved in planetary orbits.

I think that you need to open your eyes a bit wider to the true physical nature of centrifugal force. In the scenarios which you are considering, we only ever feel it passively. We can see it, but we can only ever feel it when a centripetal force opposes it. That's part of what makes some people erroneously state that it is fictitious, or that it is only a reaction to a centripetal force. But there are a few examples in nature where we can feel an active centrifugal force head on in its pure state. One such example is when we push two like magnetic poles together. You know what that feels like. That is pure centrifugal force felt directly. Another situation where you can get that exact same feeling is when you force precess a spinning gyroscope and restrain it to the rotation plane that you are force precessing it in. If you don't restrain it, it will swivel sideways. But if you restrain it, you will feel yourself pushing against the exact same kind of pressure that you feel when you push two like magnetic poles together. In the latter case, it is not technically centrifugal force in the sense of being a radially outward force. It is a mutually orthogonal sister concept to centrifugal force involving the axial deflection of a transverse motion. It is not recognized in the textbooks. It is effectively an axial Coriolis force.

Then there is the transverse Coriolis force which is effectively a transverse centrifugal force with the circulation ω doubled, due to the rigidity of space in that particular mode of motion. The transverse Coriolis force is tied up with conservation of angular momentum. If you want to feel transverse Coriolis force, you will need some difficult to make contraption involving a turntable with a radial groove with some object in outward radial motion along the groove. When you turn the turntable, you will find that you are having to put in work in order to sustain a constant angular speed, due to the outward radial motion of the object along the groove. That will probably feel something similar to pushing two like magnetic poles together, or like force precessing a spinning gyroscope and restraining it to plane of forced precession.

This entire topic is about three mutually orthogonal pressures which arise in a solenoidal dipolar field. The radial one is being masked nowadays by a hall of mirrors. The transverse one is also being masked by a hall of mirrors and it has broken loose at its hinges and been allowed to swing around in the wind like a weather cock. The axial one is not even recognized in the literature, which is why they can't explain gyroscopes and rattlebacks. David Tombe (talk) 13:47, 24 May 2009 (UTC)

You're self-evidently a crackpot. Go away and take your ridiculous OR with you. This is not the place to posit new 'theories' of physics. We've much better things to do here.- (User) Wolfkeeper (Talk) 02:09, 25 May 2009 (UTC)

Wolfkeeper, you have been a major part of the problem on this page and I'm very sorry that the administrators can't see right through you. David Tombe (talk) 11:28, 25 May 2009 (UTC)

Look, centripetal force is just the second differential of the motion with respect to an inertial frame. You set x=r cos (wt) and y = r sin (wt) and differentiate twice. You end up with an acceleration along the radius vector; and there's a force from that F=ma. Reactive centrifugal force is just Newton's third law on that centripetal force. That's all there is to it. There's no expansion, nothing. It's trivial calculus. There's no mystery. And 'fixed stars' are nothing to do with it- any inertial frame works fine, even if the stars are whizzing past your ears provided you're moving in a straight line and gravity is not too strong. This is physics that any 16 year old that has done basic calculus can handle. I don't know where you've got it into your head that this is the cornerstone to physics, but really, it's just trivial. Unbelievably trivial.- (User) Wolfkeeper (Talk) 21:10, 25 May 2009 (UTC)

Mach's principle? Mach's principle is wrong. There has never been an experiment that backs it up, and General Relativity flatly denies it. Einstein liked it, but couldn't get it to work either. Mach's principle is a guess; that failed. There is no expansion.- (User) Wolfkeeper (Talk) 21:10, 25 May 2009 (UTC)

Wolfkeeper, the equation that we are arguing about is this one,

${\displaystyle m{\ddot {r}}-mr{\dot {\theta }}^{2}=f(r)}$

It is the central force equation 3-12 from Goldstein. It contains both a centripetal force term ${\displaystyle f(r)}$ and a centrifugal force term ${\displaystyle mr{\dot {\theta }}^{2}}$. In the special case when the two are equal in magnitude, the ${\displaystyle m{\ddot {r}}}$ term will be zero and we will hence have circular motion. In the rotating frames of reference approach to centrifugal force which you seem to prefer, they are advocating that circular motion arises in conjunction with a net inward centripetal force. So something is seriously wrong. One of these two approaches must be wrong. As for Newton's reactive centrifugal force approach, it is definitely wrong because centrifugal force and centripetal force are not in general equal in magnitude. There are three approaches to this topic, and only one is universally correct. The other two approaches can be correct for limited applications. You are advocating that there are only two approaches to this topic, both different, but both equally correct. You can now see that the planetary orbital approach is a third way that conflicts with the rotating frames approach, and so the statement in the introduction which says that there are two approaches to this topic is wrong. And it has been put there deliberately as a corrupt bureacratic means of denying the existence of the third way, which is in fact the only universally correct way. David Tombe (talk) 22:11, 25 May 2009 (UTC)

All I see is a crank claiming that Newton didn't understand Newtonian mechanics, and the crank is claiming that their cranky views ought to be written into the[REDACTED] as if they were gospel fact, and they are busy trying to twist any and all references to try to support their incredibly suspect views.- (User) Wolfkeeper (Talk) 01:06, 26 May 2009 (UTC)

Wolfkeeper, There are sources cited on the main article which clearly expose the conflict between Newton and Leibniz. Leibniz succeeded in not only establishing the inverse square law for gravity, but also the inverse cube law for centrifugal force. Leibniz had an equation which put the two together and demonstrated that planetary orbits arise out of these two forces working together in tandem. Circular orbits only occur in the special case when these two forces are not equal and opposite. When the two are not equal in magnitude, then we get non-circular orbits. When Newton saw Leibniz's equation, he behaved similarly to yorself. He tried to sabotage it. He invoked the specious argument that centrifugal force is an equal and opposite reaction to centripetal force, and hence the specious 'reactive centrifugal force' concept was born. But the evidence is that Newton knew otherwise and that he was only trying to denigrate Leibniz's work. Newton knew fine well that centrifugal force is not always equal in magnitude to centripetal force. Newton only got as far as establishing the inverse square law relationship for gravity, and he was obviously intensely jealous of Leibniz for having beaten him to the full planetary orbital relationship. It's sad to see that you have been successfully fooled by Newton's 'reactive centrifugal force' concept, which was merely a jealous reaction to Leibniz's equation. David Tombe (talk) 08:13, 26 May 2009 (UTC)

Guilty as charged, I'm fooled by Newton's mechanics (actually I'm even more fooled by GR and QM). I think it's time for another ban for somebody who has been trying to get equal space for discredited theories and has been spamming talk pages over a considerable period. This is never, ever going to work. Nobody is ever going to add more than a passing mention in the history section for Leibniz anywhere in the wikipedia.- (User) Wolfkeeper (Talk) 12:52, 26 May 2009 (UTC)

Wolfkeeper, Isn't it funny then how Goldstein still uses Leibniz's equation to solve the planetary orbital problem? Here's Goldstein's equation 3-12,

${\displaystyle m{\ddot {r}}-l^{2}/mr^{3}=f(r)}$

Now imagine that equation when the centripetal term f(r) is the inverse square law gravity force. Then compare it with Leibniz's equation and tell me the difference. It's not history. You're quite wrong on that point. David Tombe (talk) 21:06, 26 May 2009 (UTC)

Never mind that trivial equation. Tell us again how Newton's third law doesn't apply in orbital mechanics problems; how the reactive centrifugal force and the centripetal force are different: "Newton knew fine well that centrifugal force is not always equal in magnitude to centripetal force."(sic).- (User) Wolfkeeper (Talk) 02:53, 27 May 2009 (UTC)

That's a bit of a red herring; nobody is claiming the reciprocal r cube term is the reactive force, right? David is referring to the fact that Newton vascillated between the different interpretations of centrifugal force, as did most others for another hundred years or so. The one interpretation, the reaction force, obviously has them equal; the other, which David is now referring to, is what Newton originally appeared to think, more like the Leibniz viewpoint, except that they didn't get the point that it only made sense in a co-rotating frame. The sources clearly indicate much confusion back then. Dicklyon (talk) 03:57, 27 May 2009 (UTC)

Thank you Dick, at least you are keeping the argument focused. As you correctly state, nobody here has been trying to say that Newton's 3rd law breaks down in planetary orbital theory. Wolfkeeper seems to think that the centrifugal force and the centripetal force are an action-reaction pair. They are not. Newton's third law holds in planetary orbits, but it holds over two bodies. Wolfkeeper doesn't understand this topic. He clearly can't grasp the second order differential equation in which the inward gravitational force and the outward centrifugal force both vary with different power laws, leading to stable conic section orbits. David Tombe (talk) 06:22, 27 May 2009 (UTC)

They are an action-reaction pair... by definition. Either you're defining it differently, fine, but we want that definition, right now, or you're denying Newton's third law, in which case you're a crank and you can STFU.- (User) Wolfkeeper (Talk) 17:26, 27 May 2009 (UTC)

Wolfkeeper, Newton's third law acts over two bodies. Centrifugal force and centripetal force are not in general equal in magnitude and they both act on the same body. Hence, on two counts, centrifugal force and centripetal force do not constitute an action-reaction pair. Nobody is denying Newton's third law of motion. You just don't know how to apply it properly. And by the way, this is one issue over which I have changed my position since this edit war began. Originally, I had not considered the concept of 'reactive centrifugal force'. When I did consider it, my first reaction was that it is an action-reaction pair. I was wrong however. At that time, your allies were quick to tell me that I was wrong. In fact I have the thread here. See how the administrator put the onus on me to provide evidence that centrifugal force and centripetal force are an action-reaction pair. But now you are putting the onus on me to produce the evidence that it isn't. I have now changed my position on that matter. You are now at variance with your ally FyzixFighter. David Tombe (talk) 18:45, 27 May 2009 (UTC)

Equation 3-12 in Goldstein

Dick, you asked me where Goldstein mentioned 'centrifugal force' in relation to equation 3-12. Page 76 in the second edition, beginning on the fourth paragraph down. He says,

"The equation of motion in r, with θ(dot) expressed in terms of l, Eq. (3-12), involves only r and its derivatives. It is the same equation as would be obtained for a fictitious one-dimensional problem in which a particle of mass m is subject to a force

f' = f + l^2/mr^3 (3-22)

The significance of the additional term is clear if it is written as mr^2 = mv^2/r, which is the familiar centrifugal force."

The form mr^2 of course appears at equation 3-11. You have been trying to insinuate that Goldstein only uses the term 'centrifugal force' in relation to the fictitious one-dimensional problem. But that is hardly likely, because we cannot possibly write it in the familiar centrifugal force format (mr^2) with an angular speed in a one-dimensional problem. You have been playing a clever game of word association. You saw the opportunity with the word 'fictitious' which bears no relationaship in the context with the fictitious force concept in rotating frames of reference.

On page 179 in the same edition, Goldstein writes,

"Incidentally, the centrifugal force on a particle arising from the earth's revolution around the Sun is appreciable compared to gravity, but it is almost exactly balanced by the gravitational attraction to the Sun. It is, of course, just this balance between centrifugal force and gravitational attraction that keeps the earth (and all that are on it) in orbit around the sun."

There is no mention of rotating frames of reference in either the first edition (1950) or the second edition (1980). However in the 2002 edition, the new editors have added an extra bit in about rotating frames of reference to justify their own prejudices. They are obviously from that generation that have been brainwashed into thinking that you can't have a centrifugal force unless you strap a rotating frame of reference around the problem.

Also on page 78 in the second edition, beginning sixth line down on discussing planetary orbits, Goldstein writes,

"A particle will come in from infinity, strike the "repulsive centrifugal barrier", be repelled, and travel back out to infinite".

In problem 8-23 on Keplerian orbits at the end of chapter 8 in the 2005 edition of Taylor, Taylor draws attention to the Leibniz equation without actually explicitly saying so. He cites the radial force equation in which the outward term is an inverse cube law force and the inward term is an inverse square law force. He then tasks the reader to show that this equation solves to yield, elliptical, hyperbolic, or parabolic orbits.

You have been trying far too hard to deny this well known topic in applied mathematics because it exposes centrifugal force as a real outward inverse cube law force, and that this conflicts with what is being taught on physics courses and in other courses in applied maths regarding rotating frames of reference. Because it was not part of your own education and because you have only just discovered it during this edit war, you are trying to distort it to fit in with your previous view of the matter, and you are not being fair to the readers. Your attitude is something along the lines of 'since I didn't know it, nobody is allowed to know it'. David Tombe (talk) 00:03, 25 May 2009 (UTC)

Thanks; in my first edition it's the same, but eq 3-12 is on page 61 and the quote about centrifugal force after eq. 3-22 on p. 64, in the section "Equivalent one-dimensional problem". The bit you quoted has the mention of "centrifugal force" a sentence or two later than the reference to eq. 3=12, and it specifically refers to a term in 3-22, on the just-introduced "fictitious one-dimensional problem".

This one-dimensional system obviously rotates its r axis to align with the planet, and the equation 3-22 is where he shows a net "effective force" in this system by adding the centrifugal force on the force side to make the "effective force" work in F = ma in that system. He calls it "the equation of motion in r", which clearly means in a system that rotates such that r-double-dot can be interpreted as acceleration in F = ma. This is all completely conventional, and there's no suggest anywhere that he refers to the centripetal acceleration term in 3-11 as centrifugal force; he's in an inertial system at that point, so he has it on the acceleration side; when he rewrites it as an equation in r only in 3-12, it's still on the acceleration side, he's just one step away from writing the F = ma in the rotating 1D system as he does in 3-22. But he's not calling it centrifugal force until after he does that; after he puts it on the force side, where he can say "The significance of the additional term is clear if it is written as mr^2 = mv^2/r, which is the familiar centrifugal force." – the reason it's clear is that it's now part of the force in F = ma, and the system in which this equation applies is the 1D system, the "fictitious one-dimensional problem" as he calls it.

There is absolutely no evidence, or reason to think, that he means centrifugal force to mean anything different from what other modern physicists interpret, which is a pseudo-force in a rotating system. Would he have called the system in whose equation of motion it appears a "fictitious one-dimensional problem" if he meant to distinguish it from the usual fictitious-force approach? I think not.

I've argued for the inclusion of this approach, sourced to both Goldstein and Taylor, and with historical roots with Leibniz. If there's a well-known topic that you think I'm denying, show us some sources. If you believe it is somehow a "third way", as opposed to a special case of the usual rotating frame analysis, show us some sources that support that interpretation. Dicklyon (talk) 17:50, 25 May 2009 (UTC)

Dick, here is equation 3-11 exactly,

${\displaystyle m{\ddot {r}}-mr{\dot {\theta }}^{2}=f(r)}$

Equation 3-12 replaces the second term on the left hand side with the inverse cube law term by substituting the angular momentum to reduce it to one variable. You are trying to tell me that the second term on the left hand side is not the centrifugal force. Can you then please name the three terms in this equation. Do bear in mind that it is the radial planetary orbital equation and it is solved to yield Keplerian orbits. And do bear in mind that Leibniz had both an inverse square law force of gravity and an inverse cube law centrifugal force in this equation. David Tombe (talk) 20:13, 25 May 2009 (UTC)

In the usual intepretation, that equation 3-11 is ma = F. The left hand side is the mass times the total centripetal acceleration, and the right hand side is the force of gravity. I'm not trying to tell you that it can't be rearranged and interpreted as just the first term being acceleration, and the second term moved to the force side and called centrifugal force – it can be; in the system that co-rotates with the planet, the fictitious 1D system as Goldstein calls it, the first term with r-double-dot is the entire mass*acceleration, and the second term is the usual pseudo force known as centrifugal force, as Goldstein points out after he does that in 3-22. Dicklyon (talk) 22:08, 25 May 2009 (UTC)

OK Dick, It's time to get to the point. Let's call the ${\displaystyle mr{\dot {\theta }}^{2}}$ term 'Harry Lime'. In order to have circular motion, Harry Lime needs to be equal and opposite to the centripetal force ${\displaystyle f(r)}$ in order for ${\displaystyle m{\ddot {r}}}$ to be zero.

In the rotating frames of reference approach to centrifugal force, circular motion arises from a net centripetal force. That is a fundamental difference between the two approaches. In the rotating frames of reference approach ${\displaystyle m{\ddot {r}}}$ is zero in circular motion, yet balanced in the equation with a net inward centripetal force. Something is seriously wrong there. Yet you are saying that these two approaches are the same. You are quite wrong on this point. The two approaches are not the same at all, and one is badly wrong. The latter approach has made Harry Lime mysteriously disappear from the equation. David Tombe (talk) 22:23, 25 May 2009 (UTC)

I haven't seen any Harry Lime in any analysis, and your attempt to introduce a new name is in no way instructive or helpful, so not clear what point you are trying to get to. In all approaches, ${\displaystyle {\ddot {r}}}$ is zero in circular motion, by definition of a circle. It's not clear to me what you're saying is different between the approaches. All of the rotating-frame approaches, including Goldstein's, have ${\displaystyle {\ddot {r}}}$ equal to zero due to a cancellation of a gravity term and a centrifugal force term when the orbit is circular, and not quite zero for other shapes. Any analysis in an inertial frame also has the same ${\displaystyle {\ddot {r}}}$ if you calculate it, e.g. by solving for it in Goldstein's 3-11, which is essentially equivalent to converting to the 1d rotating frame and looking at the acceleration (in the inertial frame, ${\displaystyle {\ddot {r}}}$ is not acceleration, as I'm sure you'll acknowledge). The fact that inertial-frame approaches do not need a centrifugal force is why such forces are called pseudo forces – they arise when making F=ma work in a rotating frame, and not otherwise. Dicklyon (talk) 00:41, 26 May 2009 (UTC)

He's not exactly doing his equation in inertial frames. Tombe is using polar coordinates and in polar coordinates the axes rotate with the body rather than at constant speed. So a 'centrifugal force' and a 'coriolis force' appear; but they're mathematically different to rotating reference frames. Tombe does not have a clue about rotating reference frames, he is apparently incapable of understanding them, but nevertheless makes sweeping claims about them; like he thinks coriolis force is always tangential to the radius vector. That's where his maths ends and crankiness starts.- (User) Wolfkeeper (Talk) 17:54, 27 May 2009 (UTC)

Dick, Equation 3-11 is,

${\displaystyle m{\ddot {r}}-mr{\dot {\theta }}^{2}=f(r)}$

Conservation of angular momentum converts the ${\displaystyle mr{\dot {\theta }}^{2}}$ term into ${\displaystyle l^{2}/mr^{3}}$. Hence, equation 3-11 becomes,

${\displaystyle m{\ddot {r}}-l^{2}/mr^{3}=f(r)}$

which is equation 3-12.

Goldstein says that equation 3-12 is the same equation as that which occurs in the fictitious one-dimensional problem because it is an equation in one variable ,r. He also points out that the significance of the inverse cube law term in the one-dimensional problem becomes clear when it is written in the form ${\displaystyle mr{\dot {\theta }}^{2}}$ which is the 'familiar centrifugal force'. So I can't see any basis at all for your attempts to deny that centrifugal force is in either equation 3-11 or 3-12. It is there as either ${\displaystyle mr{\dot {\theta }}^{2}}$, or as the inverse cube law term, and that fact is backed up by Leibniz's equation in which the inverse cube law term is the centrifugal force.

You are absolutely correct when you say that the special case of circular motion requires that ${\displaystyle m{\ddot {r}}}$ be equal to zero. But in order for it to be equal to zero we need the other two terms to be equal and opposite. Those other two terms are of course the centripetal force term and the centrifugal force term. To start with, you are engaged right now in a specious attempt to deny that one of those terms is in fact the centrifugal force term. And secondly, in your favoured 'rotating frames approach', one of your key arguments that is used to back up the extrapolation of centrifugal force to situations where a stationary object is observed in a rotating frame, involves a specious argument in which the centrifugal force is overridden by a radial Coriolis force which is twice as large, hence leading to a net inward centripetal force. In that scenario, you are trying to justify a circular motion using a net centripetal force with no equal and opposite counterbalance. If there is a net centripetal force in that scenario, then ${\displaystyle m{\ddot {r}}}$ cannot be zero. That aspect of 'rotating frames'/'fictitious forces' theory is fundamenatlly flawed and it is at variance with central force theory as per equations 3-11, and 3-12. David Tombe (talk) 07:58, 26 May 2009 (UTC)

We've been through this already. In a simple rock whirled on a string, when viewed from the NON-rotating frame (a person looking down on it, say) there is only one force, the centripetal force. This explains the non-linear motion of the rock. Whether you want to say ${\displaystyle m{\ddot {r}}}$ = 0 in this frame depends on how you define r. The scalar length of r is constant. But if r is a vector, its derivative will not be zero, because its direction is changing. So pick which ever one you like, but you can't have both. If r is the vector distance, then ${\displaystyle m{\ddot {r}}}$ is the vector acceleration, and the centripetal force provides this acceleration.

In the case of the rock which is sitting on the ground, at the same radial distance r away from you, but traveling in a circle around you because you're twirling about on your foot, and have thus chosen a rotating frame, now you have the very same distance vector, and the same acceleration vector. The scalar distance does not change, but the acceleration vector does. Again, choose which one you like! One is zero, the other is not! This acceleration (if you choose the vector, not the scalar length of the vector) is now explained by a net force, which is the net centripetal force, and which explains the fact that the rock moves in a curve, not a straight line. This force is composed of two parts-- one part is radially outward, and is the centrifugal force caused by your rotating frame. The other is radially inward and is twice as large-- the radial Coriolis force. Together they add up to a net inward force vector which is precisely the same as the vector in the first case of the rock on the string. It provides the centripetal force which explains why the rock moves in a curve in your rotating frame. That's it. You can't complain it doesn't exist because the r vector is zero-- you're talking about a scalar, there. That component is zero exactly as in the first example, if you choose r as a scalar. But if you chose r as a vector, then its second derivative is a non-zero acceleration required by the fact that the direction of the vector changes (though not its length) if you choose r as a vector. SBHarris 08:46, 26 May 2009 (UTC)

SBharris, we are looking at the equation,

${\displaystyle m{\ddot {r}}-mr{\dot {\theta }}^{2}=f(r)}$

This is equation 3-11 in Goldstein and it caters for every possible central force scenario. If ${\displaystyle m{\ddot {r}}}$ is zero, as will be so in the special case of circular motion, the centripetal force term f(r) has to be exactly balanced by an outward term of the form ${\displaystyle mr{\dot {\theta }}^{2}}$, which of course is the centrifugal force.

Originally you were instinctively aware of the fact that the Coriolis force is the transverse deflection of a radial motion in a vortex field. You knew that. Coriolis force is one of the terms in the transverse equation which contributes to the conservation of angular momentum. But you allowed yourself to be fooled by RRacecarr and SCZenz who made a private visit to you on your talk page on having seen your original heresy. You then willingly bought that nonsense about the Coriolis force swinging freely like a weather cock and being allowed therefore to swing into the radial direction. They drew your attention to the expression 2v×ω and the fact that the Coriolis force is apparently free to rotate in a plane that is perpendicular to the rotation axis. You returned to me with this new found wisdom as if I hadn't previously been aware of it and you instructed me in it like as if you were teaching me something that I had overlooked. When I showed you that the derivation of Coriolis force restricts the input velocity to the radial direction, hence restricting the resulting Coriolis force to the transverse direction, you just ignored it. You conceded 'nolere contendere' to RRacecarr and SCZenz and you then joined the majority against me.

The consequence is that you are now advocating that the Coriolis force can cause an inward centripetal force that overrides an outward centrifugal force on a stationary object as viewed from a rotating frame of reference. You do get a net inward centripetal force if you do that. But a circular motion is not the product of a net centripetal force. A circular motion arises from a net zero force in the radial direction, as per equation 3-11 above.

You are totally ignoring the centrifugal force that exists even in straight line fly-by motion relative to any arbitrily chosen point in space. A centripetal force causes curved path motion when rotation is involved. But the rotation causes a centrifugal force in the first place. In circular motion, the centripetal force merely cancels that centrifugal force. David Tombe (talk) 11:49, 26 May 2009 (UTC)

Nobody is "ignoring the centrifugal force that exists even in straight line fly-by motion relative to any arbitrily chosen point in space". It's a pseudo force that appears depending on the chosen refernce frame. For a co-rotating frame with constant angular momentum, from a point of your choice, it's the reciprocal r cube pseudo force. Who are you saying is ignoring it? Dicklyon (talk) 21:45, 26 May 2009 (UTC)

Note also that in the straight gravity-less fly by, in coordinates that rotate to follow the object from a point of view, the traditional Coriolis and Euler forces cancel each other exactly. −Woodstone (talk) 22:05, 26 May 2009 (UTC)

Woodstone is right. Additionally, read my lips: any frame which has a moving vector r, will not have dr^2/dt^2 = 0. The length of r may stay the same, but if the direction of r changes with time, its time derivative will change and thus be non-zero. So will the second derivative be nonzero. Thus, any frame in which you see the r vector MOVE in a circle (like a watchhand), will have a non-zero second derivative of r. That means your force term cannot be zero, unless the two terms cancel. Which they do if you merely look at a stationary object from a rotating frame. Or if you fly-by a stationary object, while rotating to keep your camera on it (the Woodstone case). Which causes its apparent motion to be linear, therefore inertial, therefore free of any net force. SBHarris 23:21, 26 May 2009 (UTC)

Dick, Once again, you have shown that you are one of the few that is capable of understanding this topic, but that something is holding you back from fully acknowledging your own understanding of it. You acknowledge the outward centrifugal force in straight line fly-by motion. That's good. And we all know that we get a different centrifugal force according to which point of origin that we choose.

You asked me who is denying it. Well SBharris is denying it.

You mentioned how the centrifugal force obeys the inverse cube law when angular momentum is conserved. Correct. Woodstone then reminded us all of the law of conservation of angular momentum, but without actually stating it explicitly. He pointed out how the Coriolis force and the Euler force (both transverse forces) cancel each other mathematically. We all know that he is correct on that point, but that it has got nothing to do with what we are talking about. SBharris then re-affirmed that Woodstone is correct, as if there might have been some doubt about it. SBharris even referred to the fly-by scenario as 'the Woodstone case'.

The most difficult thing to analyze above is the remainder of what SBharris has said. He makes a few very false statements. He seems to think that if the radial vector is rotating, that d^2r/dt^2 cannot be equal to zero. He then says that the force term cannot be zero, unless the two terms cancel. What can he possibly mean? He then says that the two terms do cancel if we look at a stationary object from a rotating frame. We need to look at the equation again,

${\displaystyle m{\ddot {r}}-mr{\dot {\theta }}^{2}=f(r)}$

This is the radial equation for all central force scenarios. When we have circular motion, the ${\displaystyle m{\ddot {r}}}$ term will be zero, despite what SBharris says. If it is zero, then it follows that the centripetal force term f(r) must be equal and opposite to the ${\displaystyle mr{\dot {\theta }}^{2}}$ centrifugal force term. In other words, a circular motion requires both a centripetal force and an equal and opposite centrifugal force.

Do you agree with what I have written in the above paragraph? If not, please explain. David Tombe (talk) 00:06, 27 May 2009 (UTC)

I did make a mistake. The force is not zero if you see an object in any kind of curved motion. However, if you see an object move by in linear motion, as you do if you do a fly-by of a stationary object while rotating to watch it, then the forces on the object from your rotating frame must sum to zero, since you see the object as non-accelerated (ie, traveling in a line). Hope that clears it up. Of course, you must see a net (fictitious) force moving an object in a circle around you, even if you're making it do so by rotating yourself. In that case, the f term is non-zero. SBHarris 01:16, 27 May 2009 (UTC)

SBharris, you are totally ignoring equation 3-11,

${\displaystyle m{\ddot {r}}-mr{\dot {\theta }}^{2}=f(r)}$

It's quite simple. When circular motion occurs, the inward centripetal force f(r) must be equal and opposite to the outward centrifugal force ${\displaystyle mr{\dot {\theta }}^{2}}$ in order to make ${\displaystyle m{\ddot {r}}}$ equal to zero. David Tombe (talk) 18:40, 27 May 2009 (UTC)

Let's lay off trying to teach physics to one another and just look at sources. David, the main problem with your argument is that Goldstein does not call that term the "centrifugal force" when it appears on the left side of the equation. Rather, as seen in Chapter 1 (pg 25 1st edition/pg 27 3rd edition), and as I pointed out previously, he calls it a "centripetal acceleration term". A few other sources (Taylor, Tatum, Kobayashi,etc) also use similar terminology for this term when it appears on the "acceleration side" of F=ma. I agree that this is somewhat of a misnomer, since in the inertial frame the radial (centripetal) acceleration is ${\displaystyle {\ddot {r}}-r{\dot {\theta }}^{2}}$. Goldstein only calls the term the "centrifugal force" after 3-22 when the term has been moved to the other side. This is the biggest difference between Goldstein 3-11/12 and Leibniz's equation - the inverse-cube term (Harry Lime) appears on different sides of the equation. While which side it appears on is irrelevant mathematically to the orbital solutions and I'm pretty sure you'd say which side it appears on is trivial, multiple sources indicate that it isn't trivial when describing the physics. Having the term appear on the force side of the equation, as Leibniz did, is equivalent to transforming to a rotating frame - see Taylor Ch 9, the Kobayashi 2008 reference, Whiting, J.S.S. (November 1983) "Motion in a central-force field" Physics Education 18 (6): pp. 256–257, Tatum, and the list goes on. When it appears on the other side, it's a centripetal contribution to the radial acceleration times the mass. We even have a reference that states that the Leibniz equation is equivalent to the rotating frame formulation. This understanding is also supported by "From Eudoxus to Einstein", the same book you brought up, David. It states on page 264:

"Much of the Principia is concerned with the motion of bodies under the influence of central forces or, as Newton called them, 'centripetal force'. In this we see that Newton had realized crucially that it was much simpler to consider things from a frame of reference in which the point of attraction was fixed rather than from the point of view of the body in motion. In this way, centrifugal forces - which were not forces at all in Newton's new dynamices - were replaced by forces that acted continually toward a fixed point."

Since Goldstein doesn't mention frames in the Ch 3we cannot use Goldstein to support or counter (as much as I'd love to given how explicit the other references are) David's claim that the inertial centrifugal force exists in the inertial reference frame. However, David, since we do have so many sources (including the Goldstein text itself) that disagree with your interpretation Goldstein 3-11 and that do state explicitly that the Leibniz's centrifugal force only appears in rotating frames, you need to provide a reference that says otherwise in order to claim that it is a third way. Don't argue physics, don't insult other editors, and don't cry conspiracy and suppression - just provide a reliable source that says exactly what you want to put in. We've included the "two distinct centrifugal force concepts" because we've found sources that say exactly that. Now it's your turn. Provide a source or shut up.

To everyone else, personally I find that arguing physics from first principles with David does nothing to improve the article and is an exercise in futility. Nothing anyone says here will change David's mind on the subject, but reliable sources will determine what stays and what doesn't in the article. Those magnanimous few who are still wanting to try to show David the error of his ways, or are willing to let him try to convince them the error of their ways, please take it to your personal talk pages. Here I'd rather discuss the sources. --FyzixFighter (talk) 03:18, 28 May 2009 (UTC)

Fictitious force equation

The standard one is derived in the Wiki article of the same name:

${\displaystyle \mathbf {F} _{\mathrm {fict} }=-2m{\boldsymbol {\Omega }}\times \mathbf {v} _{B}-m{\boldsymbol {\Omega }}\times ({\boldsymbol {\Omega }}\times \mathbf {x} _{B})}$ ${\displaystyle \ -m{\frac {d{\boldsymbol {\Omega }}}{dt}}\times \mathbf {x} _{B}\ .}$

The first term is Coriolus (depends on velocity v_B of the test object in the rotating frame), the second term is the centrifugal force (depends on the radius X_B only), and the third is the Euler force, which depends on how the rotational speed omega = d(theta)/dt changing, which means the value of d(omega)/dt. Here it is again, with the x replaced by r, and the subscript B's removed.

${\displaystyle \mathbf {F} _{\mathrm {fict} }=-2m{\boldsymbol {\Omega }}\times \mathbf {v} -m{\boldsymbol {\Omega }}\times ({\boldsymbol {\Omega }}\times \mathbf {r} )}$ ${\displaystyle \ -m{\frac {d{\boldsymbol {\Omega }}}{dt}}\times \mathbf {r} \ .}$

That's it. We can reduce it only a bit more for circular motion so that all the cross products come out simple products, and I can replace the omega capital with the lower case:

${\displaystyle \mathbf {F} _{\mathrm {fict} }=-2m{\boldsymbol {\omega }}\mathbf {v} -m{\boldsymbol {\omega }}({\boldsymbol {\omega }}\mathbf {r} )}$ ${\displaystyle \ -m{\frac {d{\boldsymbol {\omega }}}{dt}}\mathbf {r} \ .}$

${\displaystyle \mathbf {F} _{\mathrm {fict} }=-2m{\boldsymbol {\omega }}\mathbf {v} -m{\boldsymbol {\omega }}^{2}\mathbf {r} }$ ${\displaystyle \ -m{\frac {d{\boldsymbol {\omega }}}{dt}}\mathbf {r} \ .}$

That looks a lot like your equation, except your Coriolus term is missing entirely, as though it didn't exist as a fictitous force. My dw/dt is your d^2(theta)/dt^2, so that's your centrifugal term. But you have an dr^2/dt^2 where I have an r(dw/dt). That cannot be right. I have no idea what your term there is meant to be. It's wrong for Euler, and it's wrong for Coliolus.

Anyway, you can see how it works for uniform circular motion. dw/dt = 0, so the Euler term drops out. Because of the way I dropped out the cross products, the v left in the equation above is tangential v ONLY, as seen in the rotating frame, which means it's omega * r = -wr. (You don't even have a Coriolus term, which I think assumes that you can't even consider the case where you see a tangential v, as you would with an object you see moving in a circle around you). Note the sign for v in that direction is negative. Putting -wr for v, I get:

${\displaystyle \mathbf {F} _{\mathrm {fict} }=-2m{\boldsymbol {\omega }}^{2}\mathbf {r} +m{\boldsymbol {\omega }}^{2}\mathbf {r} }$ ${\displaystyle \ .}$

${\displaystyle \mathbf {F} _{\mathrm {fict} }=-m{\boldsymbol {\omega }}^{2}\mathbf {r} }$ ${\displaystyle \ .}$

And there we are. If I see an object circling me for no good reason (simply because I choose to pirouette), then in that rotating frame I must see a fictious force which appears to make it do that. But if I have a rope attached to it and am rotating with it, then I see it stationary. In that case, the exact same fictious force is calculated, but that is not the only force on the object. I am also exerting a centripetal force on the object via my rope, and it is m w^2 r also, but now positive because in the opposite direction. The two forces (net fictious as a result of both radial Coriolus and centrifugal forces), and the centripetal force from my rope, all add to zero. Which is good, because the object is stationary with regard to me, so can have no net force act on it from my frame. But if I don't rotate with the object but simply swing it about, all the fictious terms go to zero, and the centripetal force from my rope remains: F = m w^2 r. And that's also good, because I need a force again here to explain why this object is circling me, instead of flying off in a straight line, or sitting out there at rest (as appears when I rotate with it). SBHarris 02:53, 27 May 2009 (UTC)

In the co-rotating case, the Coriolis and Euler forces cancel each other; that is the acceleration of the frame rotation rate matches that of the theta to the planet, as it must by definition of co-rotating. The equation with difference of reciprocal r square and cube terms also depends on assuming conservation of angular momentum; in other words, only central forces. It's an elegant simplification, but not a different approach. Dicklyon (talk) 03:49, 27 May 2009 (UTC)

SBharris, I didn't miss out on the Coriolis force. There are two equations in planetary orbital theory, which is what we are talking about here. There is a transverse equation and a radial equation. Equation 3-11/3-12 is only the radial equation. It contains the centripetal force and the centrifugal force. There is not supposed to be a Coriolis force in that equation.

Yes, there is. The Coriolis force is defined by

${\displaystyle \mathbf {F} _{\mathrm {fict} }=-2m{\boldsymbol {\omega }}\times \mathbf {v} _{B}\ .}$

That cross product gives the force both radial and transverse components, depending on radial and transverse velocities of the object. A tangential velocity will result in a radial Coriolus force, and that's quite relevant here. (Radial velocities cause tangential Coriolus forces, and velocities in the spin axis direction produce no forces). So your equation for radial forces needs the transverse velocity. If it doesn't have a place for it, it's wrong.SBHarris 20:58, 27 May 2009 (UTC)

The Coriolis force and the Euler force are in the transverse equation. The two transverse terms are mathematically equal and opposite, and that leads to the conservation of angular momentum, as you already know.

Yes, but you can't just leave out one component of the Coriolis force. Do you know what a cross product is? SBHarris 20:58, 27 May 2009 (UTC)

The argument between myself and Dick is whether or not the 'rotating frames of reference' approach to centrifugal force is the same as the planetary orbital approach. I agree with Dick that in the special case of co-rotation, they are the same, although I personally don't believe that we need to bother with the rotating frames of reference. I can see what is happening perfectly well without having to strap rotating frames of reference around the problem. At any rate, I am satisfied now that Dick understands the basic principles of the planetary orbit.

You already brought in and "strapped on" a rotating frame of reference when you started to talk about centrifugal force. Since it ONLY appears in rotating frames. Otherwise, like the Euler and Coriolus force, it vanishes. If the frame doesn't rotate (which you can easily tell by whether or not the fixed stars are rotating), all that appears is centripetal force. If the stars don't rotate, just ONE arrow points at every ONE object. And which is provided by gravity in planetary motion. Or mechanically by the floor in spacestations, centrifuges and the like. That one arrow, plus the object's inertia, makes it move in a curve and that's it. No other forces enter at all.SBHarris 21:20, 27 May 2009 (UTC)

But I am not satisfied that you understand this topic at all. While I have been trying to expose the difference between planetary orbital theory and 'rotating frames' theory to Dick, you have now arrived on the scenes and attempted to undermine the planetary orbital theory by pointing out where it differs from the 'rotating frame' theory which you have copied above, as if to imply that the planetary orbital theory is wrong because of this difference. The difference which you have highlighted is in the fact that in the 'rotating frame' approach, the Coriolis force has become free to swing into the radial direction. (I don't know how that affects the conservation of angular momentum!).

Dick will of course correctly point out that this difference only applies in the non-co-rotating situation. So we are once again back to looking at the ludicrous extrapolation of rotating frame transformation equations to objects that are stationary in the inertial frame. I have told you on a number of occasions why this is nonsense, but you have completely ignored it, simply because it appears in some sources.

No, I have ignored it because what you want makes no sense. Seen in a rotating frame (or a linearly accelerating frame, for that matter), an inertial object is SEEN to travel as though it has a mysterious force applied to it! That's the whole point of introducing these "fictious forces" to begin with. SBHarris 21:20, 27 May 2009 (UTC)

So as regards Dick, I have been showing him that equation 3-12 means that centrifugal force counterbalances the centripetal force in circular motion. Dick knows that that is true.

No! It is neither "true" nor "false." It depends on what frame you choose. Only in a rotating frame (hint: the stars move) does a centrifugal force "appear" which counterbalances the centripetal force. If you think you see "centrifugal force" you've put yourself mentally into a frame where the stars go round and round! In the non-rotating intertial frame, there is no need for a centrifugal force, and it doesn't appear, so all we're left with is the centripetal force. Which is fine, because we always need a net force on an object, to explain why the object is moving in a circle!SBHarris 21:21, 27 May 2009 (UTC)

But in the ludicrous extrapolation scenario in which we observe an apparent circular motion, you are introducing nonsense on top of nonsense. First of all, you are taking a term from the transverse equation and putting it into the radial equation 3-11/3-12. That's the first piece of nonsense. The second piece of nonsense is when you then have a circular motion with a net inward centripetal force.

The last is not nonsense at all. All circular motion is caused by net centripetal force, so long as you view the motion from a non-rotating frame (so that you do indeed SEE a circular motion). Objects don't move circularly without a force. See Newton's first law. SBHarris 21:20, 27 May 2009 (UTC)

It's nonsense, but it's in some sources, and I have conceded that it is in some sources, and we were no longer arguing about that issue. My argument with Dick is that the planetary orbital approach to centrifugal force is a different approach than the rotating frames approach for the specific reason that in the planetary orbital approach, the Coriolis force is firmly fixed in the transverse direction and relates to conservation of angular momentum. In the rotating frames approach, the Coriolis force can swing like a weather cock and it is used to undermine the reality of the outward expansion effect of centrifugal force. The Coriolis force in 'rotating frames' theory is being used as a buckled spoke on a wheel to corrupt the whole picture.

The argument at the moment is that Wolfkeeper will not entertain any mention of Leibniz's approach to planetary orbital theory to appear outside the history section of the article, despite the fact that Goldstein's method is in fact Leibniz's method. Dick will entertain it but he is determined to mix it all up with rotating frames of reference and act as if it's all one and the same topic. He has also shown tendencies to want to name the centrifugal force 'the centripetal force', despite the fact that it is clear that he understands the topic sufficiently well to know that this is wrong. David Tombe (talk) 06:59, 27 May 2009 (UTC)

Generality of the planetary orbital example

The central force problem of planetary motion is not a paradigm for all discussion of centrifugal force. In fact, it is a special case surrounded by a lore that only confuses matters. It is much cleaner and more straightforward to consider simpler examples, like a ball on a string, or the rotating spheres example, which do not have a huge baggage. Brews ohare (talk) 16:35, 27 May 2009 (UTC)

Brews, Equation 3-11/3-12 is the general equation which caters for all central force problems, whether involving gravity or not. Any of your rotating sphere problems can be dealt with by using equation 3-11. David Tombe (talk) 18:37, 27 May 2009 (UTC)

Do you agree with the analysis at Rotating_spheres#General_case? Brews ohare (talk) 19:07, 27 May 2009 (UTC)

Brews, I've already looked at that bit a few times. I can't believe how complicated you have made what should be a simple problem based on equation 3-11. You have introduced two rotation speeds, yet we all know that only one of them is relevant. The only rotation speed that is relevant is the one that is measured relative to the background stars. That absolute rotation induces an outward centrifugal force which is one of the terms in equation 3-11. The centrifugal force then pulls the string taut. The induced tension in the string then causes an inward centripetal force to act, which is equal and opposite to the outward centrifugal force. The net result is circular motion.

Why can you not write it up in simple terms like that? Why all the extras about different rotation speeds and rotating frames of reference? Are you trying to mask the reality of the outward expansion? Is real outward expansion due to rotation not politically correct in modern physics? David Tombe (talk) 19:31, 27 May 2009 (UTC)

Two speeds are necessary: the rate seen by the rotating observers ω_S and the absolute speed of the spheres seen in an inertial frame ω_I, so that it can be shown that the tension can be used to establish the observer's absolute rate of rotation. Brews ohare (talk) 22:36, 27 May 2009 (UTC)

Brews, the issue of absolute rotation can be adequately demonstrated using a single rotating bucket of water. David Tombe (talk) 22:44, 27 May 2009 (UTC)

Not so. First, the rotating bucket provides a simple "yes or no" answer to whether rotation occurs, but a more quantitative answer is more complicated. The rotating sphere problem allows a quantitative answer with little complication. Second, the details of the more quantitative solution probably will lead to severe disagreements between you and the analysis presented. Those disagreements might just possibly sort things out. Brews ohare (talk) 23:07, 27 May 2009 (UTC)

Brews, could you elaborate on the disagreements that you are anticipating. David Tombe (talk) 23:16, 27 May 2009 (UTC)

For example, the article finds the fictitious force to be:

${\displaystyle \mathbf {F} _{\mathrm {Fict} }=-m\left(\omega _{S}^{2}R-\omega _{I}^{2}R\right)\mathbf {u} _{R}\ .}$

which has different direction depending upon whether the measured rate of rotation ω_S is faster or slower than the absolute rate of rotation of the spheres ω_I. Physically this change makes sense, because the measured tension must be diminished or supplemented by the fictitious contribution depending upon ω_S/ω_I <1 or >1. I seem to recall objection on your part to the fictitious force switching direction depending upon circumstance. This switch depends upon a change in the Coriolis force, inasmuch as the centrifugal force always has an outward direction.

As a particular case, if the spheres are actually not absolutely rotating (ω_I = 0), the string tension is zero and cannot explain the motion, so the fictitious force is always inward to provide the rotating observer with a centripetal force to explain the apparent circular motion.

Assuming you object still, the way forward (I'd say) is to specifically point out the mathematical step in the derivation for this result that is in error (in your opinion). That is more fruitful than a purely verbal onslaught referring to Leibniz, Goldstein etc.. Brews ohare (talk) 11:18, 28 May 2009 (UTC)

Brews, there is no such thing as a radial Coriolis force, no matter what you have read in the textbooks. I have traced this error back to Gaspard-Gustave Coriolis himself. If you don't want to believe me, that's up to you. I'm not editing on rotating frames stuff anymore. I'll leave that to you. I am interested in the real outward centrifugal force that arises in conjunction with absolute rotation. David Tombe (talk) 13:31, 28 May 2009 (UTC)

The Reactive Force and the Third Law

Wolfkeeper has been getting interested in whether or not the so-called reactive centrifugal force obeys Newton's third law of motion. Wolfkeeper believes that it does. And indeed Newton invented the concept ostensibly based on the fact that it does. It's certainly very easy to buy the idea that in the special case of circular motion that there is a centrifugal force that is an equal and opposite reaction to the centripetal force, because we know that there exists such a centrifugal force and that it is equal and opposite to the centripetal force. Even I bought this line of reasoning last year before I had time to think about it properly. And when I was the one that advocated Newton's idea, Wolfkeeper's allies were very quick to argue against me. FyzixFighter was very quick to point out that centrifugal force does not form an action-reaction pair with centripetal force in a centrifuge. At the time, I was merely drawing attention to the fact that an outward centrifugal force existed which was equal and opposite to the centripetal force, and I made the mistake of saying that the two were an action-reaction pair. Wolfkeeper still believes that they are an action-reaction pair, and Newton claimed to believe it too. But now I know that FyzixFighter was actually correct on this technicality. To have an action-reaction pair we need to consider the situation over two bodies.

FyzixFighter however now makes a mistake in that by re-inserting the section 'reactive centrifugal force' on the main article, as it now stands, he is trying to correct Newton's error. He tries to explain reactive centrifugal force in relation to two bodies in order to be right with Newton's third law. But it was Newton himself who didn't apply his own third law correctly in relation to centrifugal force. Newton merely used his third law to confuse the deeper understanding that was provided by Leibniz's equation, and so Newton shares a large part of the blame for the edit war here. To answer Wolfkeeper's specific question, Newton's third law does not break down. But the fact that we have an equal and opposite centrifugal force/centripetal force in circular motion is not an appliacation of the third law because the two central forces are not in general equal and opposite. David Tombe (talk) 23:12, 27 May 2009 (UTC)

The centrifugal force that can be not equal to the centripetal force is not the same concept as the centrifugal reaction force, which is equal by definition. Dicklyon (talk) 00:53, 28 May 2009 (UTC)

Dick, there only is one centrifugal force. The reactive concept is a faulty way of looking at it in the special case of circular motion. David Tombe (talk) 13:25, 28 May 2009 (UTC)

Break for new comment: are Coriolis forces "real"?

SBharris, There are two topics under discussion here,

(1) Planetary orbital theory, in which the Coriolis force is restricted to the transverse direction. According to that theory, Coriolis force can't be in any other direction and it is an integral aspect of the law of conservation of angular momentum (Kepler's law of areal velocity).

COMMENT. Kepler’s law of areal velocity is due to the conservation of angular momentum, for sure. But it happens just as surely to a twirling ice skater who pulls her arms in, so it’s got nothing to do with gravity, with the elipses and laws of planetary motion, or any of the rest of it.

Furthermore, it’s got nothing to do with Coriolis force per se, since in non-rotating frames, there IS NO Coriolis force. If you look at a skater in a non-rotating frame, when she pulls in her arms she’s exerting a mechanical force on them, and that accelerates them. It’s not complicated. At the base of it, it’s like seeing an object moving along in a straight line, and giving it a pull exactly transversely. When you do that, it goes faster, and in a direction which passes closer to you (over time) than if you hadn’t pulled on it. There’s no Coriolis intrinsically there, any more than there is in any situation where you pull or push an object in a direction which is not exactly in the vector if its motion. This is not Coriolis force, it’s just force of the ordinary everyday kind. Coriolis is a NEW force which comes from having a rotating observer who has to “explain” new phenomena that don’t appear if the observer does NOT rotate. If your observer doesn’t rotate, Coriolis does not operate.

Along this line, I’ve been reading above where you’re saying some really odd things about Coriolis forces operating between something traveling in an inertial line, and a point off the line that the object passes. Nonsense! If the objects are too light or the distance too great for gravity to have any significant effect, then no force operates. If gravity is strong enough to bend the object hyberbolically, then that can be explained by straight pull mechanics and inertia, and there’s no reason to bring in Coriolis, Euler, or centrifugal or centripetal labels.

In the latter case, only if the observer at the origin does something odd like rotating differentially to keep the object on the same line of sight, do you need any NEW forces. In that frame, now the incoming object behaves very oddly—coming in on a straight line directly toward the observer, then speeding up, then slowing down to a stop at a certain distance away, then immediately receeding again! All on the same line! That requires a lot of new forces to produce that motion—gravity alone will not do it. But they’re all a result of insisting on rotating the observer.

Once again, Coriolis force does not even exist, unless you have put yourself in a rotating frame. That’s YOUR big error. If you’re in a frame where the stars are fixed, there’s no Coriolis force. There’s only the standard forces of nature, which act according to Newton’s laws. No “standard force of nature” would cause an object to approach you, stop, then retreat, on the same line, without rockets or any other drive. To have that happen inertially requires something other than the pull of gravity. But if you don’t rotate, the pull of gravity suffices to describe the motion perfectly well. (All singley-indented answers are from SBHarris 01:52, 28 May 2009 (UTC))

(2) Rotating frames of reference/Fictitious forces. Modern textbooks have allowed the Coriolis force to be free to swing into the radial direction. I personally believe that that is a big mistake, but that is not the point at issue here. The point at issue is whether or not these two approaches to centrifugal force are the same. I say that they are different, for the very reason that in (1), Coriolis force is restricted to the transverse direction and tied up with Kepler's second law, whereas in (2), it is free to be in the radial direction also. You have now entered this discussion and drawn attention to what we all knew already. We know that the modern topic of fictitious forces allows for the Coriolis force to be in the radial direction. If you want to believe that, that's your problem. You think that you are being very clever when you point out the expression in vector product format and ask me if I am familiar with vector products. But you have wilfulfully ignored the derivation of that expression and the restriction that is inherent in it. And you keep repeating this error over and over again.

COMMENT. Hey, it’s not my derivation. But it is a perfectly good one. The derivation given is HOW WE DEFINE “Coriolis force” and the other fictious forces. And how they’ve been defined for centuries. If you want to write Tombe’s Textbook of Physics and have a Tombe Force which is different from Coriolis and only acts transversely/tangentially to a body’s motion, and never has a component which is radial, that’s fine. Go for it. But here on Misplaced Pages we’re talking about the Coriolis Force, not the Tombe Force. One fictitious force at a time, please.

The question is , 'why do we have one topic which clearly restricts the Coriolis force to the transverse direction and ties it up with Kepler's second law of planetary motion, whereas in another topic, the Coriolis force is free to be in any direction in the plane perpendicular to the rotation axis?'

And the answer is: that you assume facts not in evidence, because the Coriolis force is NOT tied up with Kepler’s laws of planetary motion or any other kind of motion (including the skater’s arm motion). The Coriolis force does not appear in any form unless you rotate your observer against the background of fixed stars. Until you do that, skaters and planets and all manner of systems can be described without recourse to Coriolis or Euler or centrifugal forces. In fact, no fictious forces of any kind are needed to describe their correct paths. Just the force of gravity, acting by Newton’s second and third laws, is quite sufficient. What you choose to call that force is up to you. You can call it “centripetal” if you like, just as you would in a centrifuge or a rotating space station (it’s what pushes up on the shoes of the astronaut). This one force is what keeps the planet from going off in a straight line ala Newton’s first law (and does the same for the astronaut). But no other force on the planet is needed if your observer does not rotate. There is no centrifugal force because the planet is moving in a curve, not moving in a line, so two forces adding to zero are not needed. And yes, the planet pulls on the Sun, but that’s not a new force ON THE PLANET (a force in the planet’s free-body diagram, which contains just one force). That’s the OTHER END of the force vector arrow, ala the 3rd law, and it applies to the SUN. It’s not fictitious, either.

I suggest that you now go to the central force chapter in Goldstein, and show us all how within the context of that chapter, the Coriolis force can walk out of Kepler's second law of planetary motion and walk into the radial equation at 3-11. When you can do that, then I'll believe Dick that these two approaches are one and the same topic.

Why would I want to do that? If Goldstein thinks that Coriolis force exists in systems which do not rotate, then he’s at odds with the definitions of modern physics also, and thus there’s no point in arguing with him over what Coriolis force is. The modern definition of Coriolis force is given above, and it exists only in rotating systems. Even using it in a system as simple as an incoming hyperbolic comet results (if you rotate in a somewhat trickily varying way, to keep the same line of sight between the objects) in a need for 3 new forces besides gravity to explain the very physically odd behavior of an object which 1) stays on a line but first approaches at a constant velocity, then 2) approaches faster, 3) slows, 4) stops, 5) recedes again, 6) recedes faster, and then 7) finally receds at a constant rate, once again. For a planet, it’s similarly irritating to watch it from constant line of sight, even if you’re on the primary (like the Sun). You can do it, but using the example of a planet or comet (where the rotation rate must be varied, introducing yet MORE complications) instead of a circling ball, adds no insight into fictitious forces at all, and only needlessly complicates the issue.

The punchline is that the fictitious forces topic has got it badly wrong. In a cyclone, the Coriolis force is a real transverse force that deflects the inward radial motion into the transverse direction. It is tied up with conservation of angular momentum. But in modern 'fictitious forces' study, the Coriolis force has somehow come to refer to the apparent transverse deflection that is observed from a rotating frame of reference. That entire topic has become loose at its hinges. But that's your problem if you want to believe it.

No, the punchline is that you believe that in a cyclone, exactly as with a skater, the translation of inward motion to faster “spin motion” (tangential rotation) is somehow connected to “Coriolis force” when in fact it has nothing whatsover to do with it. In a cyclone as in a skater, when you pull on something going by you, it goes even faster! Wow, call Physics News. That is Newton’s second law and it involves forces not fictitious (this is the only thing we agree on, probably). Coriolis forces only appear if you insist on viewing this situation (cyclone or skater or planet) from a rotating frame (where the fixed stars rotate also). But you don’t need to CHOOSE to do that. The arms of the skater and the winds of the cyclone still go faster when you pull them, but no fictitious forces are involved, because they may (if you wish) be banished by mere choice of coordinate system. The physics is all the same, if you just say “no”! I’m going to call this the Nancy Reagan Law of Coriolis Force.

Just don't try to tell us that it's all the same topic as planetary orbital theory. I copy out the radial equation 3-12 from Goldstein and you come along trying to tell me that I have left out the Coriolis force, and you try to justify it by copying out a pile of equations from another topic about rotating frames of reference? You basically just pushed Goldstein's chapter 3 aside and brought in another topic, and then claimed that Goldstein's chapter 3 is wrong because the Coriolis force doesn't appear in the radial planetary orbital equation at 3-12. David Tombe (talk) 22:42, 27 May 2009 (UTC)

Have it your way, then. But however you have it, please be assured that Coriolis force can always be removed by choosing your observer to be non-rotating with regard to the fixed stars. If you refuse to do that, the problems in store for you are your problem. Please don’t come here and tell us that they have to do the reality of WHY things happen. And as for describing how they happen, or the easiest way to calculate that, please stick to historical definitions, not your own. SBHarris 01:52, 28 May 2009 (UTC)

So much nonsense. Coriolis force is purely transverse when the motion is purely radial, as in the co-rotating frame. That's all. Dicklyon (talk) 00:54, 28 May 2009 (UTC)

There is a term in polar coordinates that always acts transverse (acts on the angular rotation) that is sometimes referred to as coriolis see (Polar_coordinates#Vector_calculus). That's Tombe's problem- he only understands the polar form; in the orthogonal vector form the coriolis force there can point in any direction. So it's not a planetary thing per se, it's polar. It's just that orbits are traditionally analysed using polar coordinates.- (User) Wolfkeeper (Talk) 12:46, 28 May 2009 (UTC)

I think that this article should probably mention the polar form of centrifugal force, as it's not quite the same as reactive or rotating reference frames.- (User) Wolfkeeper (Talk) 12:46, 28 May 2009 (UTC)

Wolfkeeper, it's an inertial effect. Polar coordinates are only a language used to describe it. It is the one and only Coriolis force and it is a transverse effect which conserves angular momentum. It can be felt directly when we try to restrain a rotating radial motion. As regards introducing a third approach to centrifugal force in this regard, that's exactly what I have been trying to do. But it is not a different centrifugal force as you seem to be suggesting. It is the most general way of looking at the one and only centrifugal force. David Tombe (talk) 13:24, 28 May 2009 (UTC)

Nah, there's 3 different equations for centrifugal force:

• reactive centrifugal force (omega is the angular speed around the rotation centre, which is not necessarily stationary)
• rotating reference frames centrifugal force (omega is the frame rotation)
• polar coordinate centrifugal force (omega is the particle angular speed in the reference frame)

Reactive centrifugal force is always equal and opposite to another force.

Rotating reference frames centrifugal force appears when the frame is rotating.

Polar coordinate centrifugal force appears when the object moves around the origin (this can occur in addition to the rotating reference frame centrifugal force if the reference frame is rotating as well.)- (User) Wolfkeeper (Talk) 13:29, 28 May 2009 (UTC)

I think the polar coordinates analysis should be thought of not as a different approach, but some math that helps to connect the inertial frame analysis to the rotating frame analysis. In the polar coordinates, it's easy to take a centripetal force or acceleration in the inertial frame and move it across to be a centrifugal force in the rotating frame; you get Coriolis forces a the same time. The relevant term is not the reactive centrifugal force, except that it happens to match in the case of circular motion. The reaction force approach remains distinct; it's about an outward force on the body causing the curve path, not on the particle in the curved path. It's too bad both use the same name, but that's the way it's been since Newton and his supporters; as Meli say, "Newton's theory of centrifugal force followed a case-by-case pattern." Basically, different coordinate systems can lead to very different equations, but they don't mean different things. Dicklyon (talk) 15:41, 28 May 2009 (UTC)

Wolfkeeper, those are three different approaches to centrifugal force. Are you going to side with me now against dicklyon and FyzixFighter who have been trying to suppress references to the third kind? David Tombe (talk) 13:36, 28 May 2009 (UTC)

No offense intended Wolfkeeper, but I disagree with you on the three types idea. And David, just because Wolfkeeper or any other editor thinks there's three does not mean that we get to put that in the article. Sources determine what goes in the article, not our opinions and original thoughts. Do we have any references that distinguish between the rotating frames and polar coordinate concepts? I would argue that Taylor Ch 9 and the Kobayashi reference indicate that the polar coordinate concept is a special case of the rotating frame concept, specifically that of a co-rotating frame. Even if I do come around to the idea, given that we have two references that say that there are two valid and distinct concepts of centrifugal force, we need another reference to say that there is a third distinct concept. We have some references that call the ${\displaystyle -r{\dot {\theta }}^{2}}$ term in the radial acceleration the "centripetal acceleration term" or something similar. Are there references that call it the centrifugal force when it appears on the acceleration side of F=ma? --FyzixFighter (talk) 14:03, 28 May 2009 (UTC)

They can be considered to be logically distinct because the omegas in each case are different. You're right that the rotating reference frame and polar coordinates are similar and highly related, but the coriolis force in polar coordinates and rotating reference frames points in different directions- the equations these are terms in are very different. You can make a rotating reference frame behave the same as polar coordinates, rotating reference frames are more general. There's also a point about coordinate systems and reference frames being logically different though.- (User) Wolfkeeper (Talk) 14:16, 28 May 2009 (UTC)

There's also practical problems with asserting that there's only two, because a lot of people reading the[REDACTED] won't have been exposed to rotating reference frames, whereas polar coordinates are widely taught. So even though it can be considered more or less a special case, it's not that helpful to treat it entirely that way.- (User) Wolfkeeper (Talk) 14:16, 28 May 2009 (UTC)

I agree with you on the Coriolis force comment. Taylor does as much, calling it the "Coriolis acceleration" (pg 29). Taylor does connect it up with the rotating frame concept in chapter 9 via the co-rotating frame.

I might be able to say that the polar coordinate concept is more closely tied to d'Alembert's principle, but most texts treat that as equivalent to the rotating frame formulation - to the point that we call fictitious forces d'Alembert forces. Kobayashi argues that there is a subtle difference, but ultimately lumps the two together, again the d'Alembert principle being the special case of co-rotating frame with axis at the origin. Note that in the corotating frame, the two omegas by definition are the same, but you are right that the general rotating frame formulation works even when the two omegas are not the same, in which case d'Alembert's effective equipollent force is not the same as the rotating frame's centrifugal force. An in-depth discussion of the subtlety would probably be more appropriate on the Centrifugal force (rotating reference frame) article rather than on this summary article.

Nevertheless, a source would be helpful. I ask this of David, and it would be unfair for me not to ask this of others and of myself. Let's not dumb down the subject to the point of being wrong. We have sources for the rotating frame and the reactive concepts, let's get a source for the polar coordinate one and try find an equitable compromise to include everything with a valid source. --FyzixFighter (talk) 14:48, 28 May 2009 (UTC)

There are only two equations involved in this entire topic

FyzixFighter, It's because of interventions such as that by SBHarris that we need to understand the physics as a priority before we can write a coherent article. We cannot, as you have just suggested, write a coherent article based on a patchwork of conflicting sources. Unlike SBharris, you do at least appear to have grasped the essentials of the topic, but you are playing silly games with names and references. We have two equations to consider in central force theory and these two equations totally describe the inertial path.

There is a radial equation which in essence is Goldstein's equation 3-11, with gravity inserted for the centripetal force,

${\displaystyle {\ddot {r}}=-G(M+m)r^{-2}+r{\dot {\theta }}^{2}}$

It is essentially Leibniz's equation. It contains the gravitational attractive acceleration (inverse square law), and the centrifugal repulsive acceleration. This solves to give a conic section inertial path. Kepler's first law of planetary motion is an example of this.

Then there is the transverse equation,

${\displaystyle 2{\dot {r}}{\dot {\theta }}+r{\ddot {\theta }}=0}$

The transverse equation follows from Kepler's second law of planetary motion. It contains the Coriolis force and what you guys have been referring to as the Euler force. We can use the transverse equation to make the centrifugal force in the radial equation into an inverse cube law term in line with Leibniz's equation. The significance of the transverse equation is clear. In a cyclone, the inward radial motion will be deflected into the transverse direction. That is real Coriolis force as in an object following its inertial path. Rotating frames of reference don't enter into it. They are just an additional complication.

While you and Dick understand this, you are playing silly games. You are trying to deny the names of the terms, even though I have already produced sources which apply the names centrifugal force and Coriolis force to the respective terms in these equations. Dick is fixated on the fact that the Coriolis force is only restricted to the transverse direction in the special case when the inducing velocity is radial. But it can't be any other way. There is no provision in nature for it to be any other way.

SBharris clearly doesn't understand the topic at all. He tried to tell me that equation 3-12 in Goldstein is wrong because it doesn't contain a Coriolis force term. He didn't realize that the Coriolis term is in the transverse equation, and he is clearly incapable of seeing how it links in to the conservation of angular momentum. He has just tried to tell me above that the Coriolis force has got nothing to do with the conservation of angular momentum. The idea of writing[REDACTED] articles is to inform people. But your deliberate attempts to obstruct me in that regard have given the green light to people such as SBharris, who clearly haven't got the first clue about the subject, to come in and join your group and make themselves believe that they have got something positive to contribute to the article. David Tombe (talk) 13:18, 28 May 2009 (UTC)

As I said before, there is a subtle distinction between Leibniz's equation:

${\displaystyle {\ddot {r}}=-G(M+m)r^{-2}+r{\dot {\theta }}^{2}}$

and Goldstein 3-11/12, namely that Harry Lime is on different sides of the equal sign. As indicated by multiple references, when Harry Lime is on the other side it's part of the radial acceleration and the equation is for an inertial frame (Goldstein calls it a centripetal acceleration term). The sources also indicate that moving Harry Lime to the side that Leibniz writes it on corresponds to transforming to a rotating frame where it becomes the centrifugal force associated with that rotating frame.

As for comments on sources, I don't recall you providing any sources that apply the name centrifugal force to that term in the inertial frame. The sources we are using do not conflict, only your interpretation of them does. Again, provide sources that explicitly say what you want to include and we'll get along. The idea of writing[REDACTED] articles is to inform people using reliable sources, not using our own personal theories on the subject. Appealing to reliable sources allows us to easily correct mistaken ideas. I'd recommend that Sbharris take a look at the Whiting letter I mentioned above and the Kobayashi reference for a clear explanation of what I think he is trying to discuss with you. --FyzixFighter (talk) 14:24, 28 May 2009 (UTC)

FyzixFighter, I can see that you do now understand the topic. But you must realize that I am simply not going to buy the idea that a centrifugal force can become a centripetal force simply by shifting it to the other side of an equation, even if there are misinformed references that imply that. Dick also appears to understand the topic, but he has shown serious tendencies to want to follow up that idea about changing centrifugal force into centripetal force by changing it to the other side of the equation. So long as you and Dick can use confused references to confuse the topic, then we are not going to get anywhere.

Let's compare a few positions.

(1) Wolfkeeper. He has identified correctly that all is not the same as between the rotating frames approach and what he terms the polar coordinates approach.

(2) Dick. He claims that the two overlap in the special case of co-rotation.

My own position as you already know is that the rotating frames approach is total nonsense when it is extrapolated to non-co-rotation situations. This then leaves a large degree of agreement between myself, Dick, Wolfkeeper, and probably yourself as regards the underlying physics behind the co-rotation situations.

As regards co-rotation, I am advocating that we simply don't need to involve rotating frames of reference at all, and I have pointed to Goldstein as a gold standard reference which treats the inertial path without any reference to rotating frames of reference. My own view on all of this is that centrifugal force and Coriolis force are built into the inertial path. Wolfkeeper doesn't quite see it in such simple terms. Wolfkeeper rationalizes with it in terms of polar coordinates. Now I am all in favour of polar coordinates because they are the only viable language for expressing central force problems in. But centrifugal force is not a product specifically of polar coordinates, as Wolfkeeper seems to think. Centrifugal force and Coriolis force are properties of space. We get different centrifugal forces and Coriolis forces when we choose different point origins, and in that respect they are 'relative' quantities. But they are also absolute in the sense that absolute rotation relative to the background stars is what determines their value for a chosen point of reference. Such is the nature of space.

Rotating frames of reference have actually totally messed this subject up. And although I acknowledge that most of the modern textbooks on the science library shelves promote centrifugal force as being something that is only observed in a rotating frame of reference, there are still a few left which don't take this approach.

In my opinion, centrifugal force and Coriolis force are inertial forces and they don't need to be understood in terms of rotating frames of reference. I have got a few sources to back that idea up. I suggest that we totally remove the reference to 'two' approaches to centrifugal force in the introduction, because the literature clearly talks about at least three approaches. David Tombe (talk) 16:46, 28 May 2009 (UTC)

Start providing the sources then so that we can discuss them. As the 'two' approaches in the intro are supported by two references, removal of such and/or inclusion of a distinct third approach requires another reliable source that explicitly says as much. While you may believe the references are misinformed, they pass wikipedia's criteria for reliable sources, thus the viewpoint they contain goes in the article. NPOV says that we report all significant, verifiable viewpoints supported by reliable sources. --FyzixFighter (talk) 17:11, 28 May 2009 (UTC)

FyzixFighter, we can start with Shankar 1994 . Here is a clear reference to centrifugal force outside of the context of rotating frames of reference. But I'm sorry that you have chosen to play this silly game. I'm trying to make the article correct and readable. You think you're playing a clever game by using the many conflicting sources in the literature to undermine what I'm trying to do.

And just for good measure, on page 179 in Goldstein (second edition (1980) before Poole and Shaftoe got the hold of it in 2002) writes,

"Incidentally, the centrifugal force on a particle arising from the earth's revolution around the Sun is appreciable compared to gravity, but it is almost exactly balanced by the gravitational attraction to the Sun. It is, of course, just this balance between centrifugal force and gravitational attraction that keeps the earth (and all that are on it) in orbit around the sun."

There is no mention of rotating frames of reference in either the first edition (1950) or the second edition (1980). However in the 2002 edition, the new editors have added an extra bit in about rotating frames of reference to justify their own prejudices. They are obviously from that generation that have been brainwashed into thinking that you can't have a centrifugal force unless you strap a rotating frame of reference around the problem.

Also on page 78 in the second edition, beginning sixth line down on discussing planetary orbits, Goldstein writes,

"A particle will come in from infinity, strike the "repulsive centrifugal barrier", be repelled, and travel back out to infinite". Some illusion! David Tombe (talk) 17:22, 28 May 2009 (UTC)

Sorry but these do not support what you are trying to put into the article. Specifically they do not support the statement that the centrifugal force exists in the inertial frame. Lack of discussion of rotating frames is not the same as confining the discussion to an inertial frame. Especially when we have multiple other references that do the same analysis and explicitly state the transformation from an inertial to non-inertial frame.

For example, Shankar doesn't mention frames - so we cannot say that he supports the statement that the centrifugal force exists as a real force in an inertial frame. Note that he also refers to them as terms and not forces. This is probably due to the fact that he distinguishes between generalized forces and real forces. See his comment on the previous page:

"Although the rate of change of the canonical momentum equals the generalized force, one must remember that neither is p_i always a linear momentum (mass times velocity or "mv" momentum), nor is F_i always a force (with dimensions of mass times acceleration)."

As to the Goldstein references, since Goldstein makes no comments about frames, he also cannot be used to either support or contradict your assertions. I would argue that Goldstein's description of the centrifugal force as the "reversed effective force" of the centripetal acceleration supports the "fictitious" designation per D'Alembert's principle. Also, your throwing out of the 2002 edition is unacceptable - if you disagree, we could always ask an admin to weigh in or to tell us what the criteria is for throwing out a reliable source. The editions are not mutually exclusive if you accept that no statement of a reference frame does not imply an inertial frame. I also object to your characterization as the rotating frame as a recent paradigm shift. As already indicated by one of the historical references, Lagrange stated it specifically that the centrifugal force is due to the rotating coordinate system and not inherent to the motion of the particle. Also, I've been able to find a 1904 reference that agrees with the rotating reference frame formulation (Whittaker, "Analytical Dynamics", 1904). Speaking of going from a inertial system to a rotating system, he states on page 41, "The term centrifugal forces is sometimes used of the imaginary forces introduced in this way to represent the effect of the enforce rotation."

If you disagree with my assessment of the sources, the best thing to do would be to get a third opinion or put request in over at the Reliable sources noticeboard to get some uninvolved editors/admins to comment. --FyzixFighter (talk) 18:43, 28 May 2009 (UTC)

FyzixFighter, we already know that the adminsitrators have been totally fooled by you. We saw the kind of comments that they made on the noticeboard when I went there to report you for wiki-hounding. I have given you reliable sources to show that it is not necessary to involve rotating frames of reference when considering centrifugal force. You have managed to present some false counter arguments that could only be swallowed in this particular arena. There are other editors here who can't agree amongst themselves, but for whatever reason, they have a mutual pact to make sure that they will religiously disgree with whatever I say, whether it is sourced or not. You are playing silly games at the expense of the reader. My suspicions are that you have got some vested interest in hiding the truth surrounding this topic. David Tombe (talk) 18:52, 28 May 2009 (UTC)

David, I've been trying to restrain my tendency to express my feelings when discussing technical topics, but just for the record, let me say that you are completely "full of crap". That's a technical term, like "bullshit", only more so. Enough said. Dicklyon (talk) 18:57, 28 May 2009 (UTC)

No Dick, you and FyzixFighter have both got the same agenda. You are trying to mask the reality of the outward expansion that comes with absolute rotation, because it doesn't fit your own pet theories about relativity. You are breaking all the rules here and getting away with it because you have fooled the administrators. I have just presented some sources, and what you have just written above is the best that you can reply to them because you know fine well that you are in the wrong. You clearly understand this topic, but you have also been clearly trying to distort it. You want the article to be confused. David Tombe (talk) 19:03, 28 May 2009 (UTC)

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