Talk:Holonomic/Archive 1

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I'm not sure, but is it correct to define a holonomic coord system as a holonomic section of the (second) jet bundle? Details would be nice.linas 02:56, 24 Jan 2005 (UTC)

All differentiable coordinate systems (without critical points) are holonomic. Hence the identification of coordinate basis with holonomic basis, by the Frobenius theorem. So I deleted the references to spherical and cylindrical coordinates as being non-holonomic because they were misleading. Consider looking into holonomic and nonholonomic pseudocoordinates.

Furthermore, it's quite difficult to define the adjective holonomic in general to everyone's satisfaction. So this should probably be a disambiguation page anyway. Jholland 05:07, 12 May 2005 (UTC)

Robotics

The section on robotics is incoherent. Holonomy and nonholonomy are used in robotics in the same way as in mechanics: a constraint is holonomic if it can be expressed as a function of joint/pose positions. It's nonholonomic if it involves velocities, and cannot be integrated into a constraint on positions alone. A robot is called nonholonomic if it has nonholonomic constraints.

I recommend removing the section on robotics, since it is an application of the concepts from mechanics

(see, e.g., the comprehensive reference book "Nonholonomic Mechanics and Control" by Anthony Bloch.)

Overmycketsjal (talk) 05:47, 17 January 2008 (UTC)

I would agree - for example, realistically, wouldn't ballbot have constraints on it's motion dependent on velocities? I thought that rolling without slipping was the canonical first example of a nonholonomic system (see Robot Modeling and Control by Spong, Hutchinson and Vidyasagar).

Fehknt (talk) 20:19, 18 July 2008 (UTC)

The reference that uses the "robotic" definition of holonomic/nonholomic is George Bekey's Autonomous Robots, on pg 194. This is just plain wrong, and all other references I have looked at use the term per the standard definition (Dudek, Jenkin's Computational Principles of Mobile Robotics, and LaValle's Planning Algorithms to name two). (Steven Waslander, September 21 2010). —Preceding unsigned comment added by 129.97.120.143 (talk) 16:44, 21 September 2010 (UTC)

Definition of holonomic

This article is the prime example of a fundamental deficiency in virtually all of Wikipedia's math articles. Definitions are just terrible. How can you define a holonomic system as a system which is holonomic? Honestly, that's just balderdash! Please don't pontificate about being mathematically rigorous. Wikipedia is an encyclopedia, not a math textbook. Mathematicians do not come to a general encyclopedia when they are researching a problem. Presumably, the intelligent layman is the target audience for articles such as these. Mathematical terms need to be defined descriptively, and the concepts they represent need to be explained in an adequate manner before the mathematical rigor is presented. No, it is not true that mathematical concepts can only be expressed with formulae. Every mathematical statement or idea has an abstract concept behind it, and it can be expressed in words or analogies. Yes, it is extremely difficult to do so at times, but many authors, such as John Gribbin in physics and cosmology, and John Derbyshire in mathematics, have shown that it is entirely possible to present arcane mathematical concepts with a measure of comprehensibility. I am not a good enough mathematician to do this either, but SOMEONE needs to clean up these articles, or at least add enough descriptive exegesis to make these articles comprehensible to the general educated public.74.239.2.104 (talk) 15:54, 16 December 2008 (UTC)

Coordinate basis ≡ holonomic basis?

It is clear that a coordinate basis is a holonomic basis (on a chart). The converse is presumably true, i.e. that for any holonomic basis there exists a chart such that the basis is also a coordinate basis (meaning isomorphic to the basis of the tangent space defined by partial derivatives of the chart coordinates). Can this be stated with a reference? I am having no luck on Google. — Quondum^☏ 16:53, 2 August 2012 (UTC)