Talk:Nonholonomic system

message: 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)
thread_title: A corollary and some examples do not yield a definition

message: 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)
thread_title:  Some new material 

message: 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)
thread_title:  Foucault's Pendulum 

message: 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)
thread_title:  Article still needs work 

message: 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)
thread_title:  Example of sphere too abstruse 

message: 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)
thread_title:  Classification problem 

message: 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)
thread_title:  Definition is Wrong