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These examples are too hard to figure out because they do not provide any figures nor any equations. It would be like the articles on calculus without pictures or equations... I don't doubt that the kinematic constraints on a unicycle wheel are nonholonomic or that without knowing the time history of its internal coordinates that I would lose track of its position. However, I need a little more proof about how a nonholonomic (non-integrable) constraint leads to this condition. ChrisChiasson 16:01, 22 September 2007 (UTC)
Following the citation needed link, I was encouraged to be bold. So I will, but the edit will basically just dump a bunch of new material into the document. Since I am not likely to return to this, I leave it to others to format it, arrange it, and blend it into the stub. The bulk of the contribution will address the incomprehensibility issue raised by Chiasson above.
As a general remark, I find scientific/mathematical wikipedia articles about which I have some knowledge tend to focus more on erudition than pedagogy, leading to obfuscation instead of clarity. This, it seems to me, defeats the purpose of an encyclopedia, which is to concisely summarize and communicate an understanding of a topic in contrast to the proforma mathematical expression of the underlying ideas. This leads me to believe that the depth of understanding of many of the scientific/mathematical editors is not great, which is an unfortunate discredit to the credibility of the wikipedia in topical areas where my ignorance is greater. 20 April 2008
Having now completed the editing, I also deleted the references to "sub-Riemannian manifolds" which strike me as dubious. In addition, I deleted all of the material which bothered Chiasson, as that material was, at the very best, vague, and in places was quite misleading. The examples I entered are far more complete, instructive, and intuitive, so they more than make up for imprecise words about cars, bicycles, and unicycles.
I put in a title "Constraints" over the previously entered equations, and, while they may be correct, I in no way endorse them. I simply do not deal with anholonomies in such general mathematical terms, and my suspicion is that these equations and their description are at least incomplete and may in fact be incorrect. 20 April 2008
Foucault's Pendulum
I doubt this claim: "The anholonomy induced by a complete circuit of latitude is proportional to the solid angle subtended by that circle of latitude". Or I misunderstood it. When the pendulum is at the pole, then the angle subtended by the circuit of latitude is 0, but the pendulum makes a complete turn about its vertical axis relative to the earth's frame.
Gabriel ( talk) 16:32, 11 June 2012 (UTC)
The anholonomy is the deviation that remains upon return to the starting point. At the pole, the deviation is zero. The fact that the pendulum visibly moves in the intervening 24 hours is moot - the residual deviation is zero - the plane of oscillation is the same at the start and at the end.
In contrast, at the equator, the solid angle subtended by the path is 2*pi. If the proportionality constant is one, which I believe it is, the anholonomy at the equator is equivalent to zero. The tendency of the Foucault pendulum is to precess more slowly with larger solid angle. In the equatorial case, there would be no visible motion in the intervening 24 hours, yet the anholonomy is non-zero but equivalent to zero. — Preceding unsigned comment added by 174.1.146.124 ( talk) 21:02, 26 March 2014 (UTC)
The whole introduction reads kind of mystically. It's very verbal. It reads like Hawking and Ellis, beautiful from a literary point of view, but you have to do all the math in your head... The difference is that Hawking and Ellis gives you the tools to do so. It's hard for a mathematician to figure out what the formal definition might be or what's meant. 129.132.211.144 ( talk) 10:49, 24 May 2017 (UTC)
The sphere example is intended to be simple, but is written in a horribly mathematical way. Some mathematical examples are needed, but the simple example would be better with a 2D example, or (better yet) a wheel.
Improved 'simple' example: a bicycle or a car. Initially the inflation valve is at a certain position. Ride/drive it around, and park it in exactly the same place. The valve is almost certainly not in the same position as before, and its new position depends on the path taken.
—DIV (
137.111.13.48 (
talk) 01:16, 24 April 2019 (UTC))
This title startled me : so I checked and there is already an article about Holonomy into which this content should merged, and Nonholonomy or Anholonomy, along with the systems that bear this property, should redirected there. Also, Nonholonomy and Anholonomy look like synonyms, but there seems to be a distinction if you look at this title : "Anholonomic frames in Nonholonomic mechanics" (find in G-search top result), a paper which I admit is far too mathematical for me. I think that clarifying these points in terminology would also be useful. Zigomar7 ( talk) 19:35, 15 October 2019 (UTC)
Sorry to say so but the definition is clearly misleading rubbish. Unless you distinguish precisely between unconstrained state space and constrained state space notions, this will also just remain rubbish. State always depends on the path taken to arrive at it if you employ large enough state space concepts (and this also is true for misleading unicycle example). The article lacks a description of the fundamental notions needed to describe the phenomenon! — Preceding unsigned comment added by 2001:638:804:1FF:1000:0:0:56 ( talk) 00:03, 20 January 2022 (UTC)