Nonholonomic Hamilton-Jacobi equation and Integrability

Details Nonholonomic Hamilton-Jacobi equation and Integrability Nonholonomic Hamilton-Jacobi equation and Integrability

2009-06-18

arxiv.org/abs/0906.3357v4

Journal of Geometric Mechanics, 1 (2009), pp. 461-481

Physics

Mathematical Physics

16 pages, 3 figures, submitted to Journal of Geometric Mechanics

Scientific paper

10.3934/jgm.2009.1.461

We discuss an extension of the Hamilton-Jacobi theory to nonholonomic mechanics with a particular interest in its application to exactly integrating the equations of motion. We give an intrinsic proof of a nonholonomic analogue of the Hamilton--Jacobi theorem. Our intrinsic proof clarifies the difference from the conventional Hamilton-Jacobi theory for unconstrained systems. The proof also helps us identify a geometric meaning of the conditions on the solutions of the Hamilton-Jacobi equation that arise from nonholonomic constraints. The major advantage of our result is that it provides us with a method of integrating the equations of motion just as the unconstrained Hamilton--Jacobi theory does. In particular, we build on the work by Iglesias-Ponte, de Leon, and Martin de Diego so that the conventional method of separation of variables applies to some nonholonomic mechanical systems. We also show a way to apply our result to systems to which separation of variables does not apply.

Affiliated with

Also associated with

No associations

Rating

Nonholonomic Hamilton-Jacobi equation and Integrability does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Nonholonomic Hamilton-Jacobi equation and Integrability, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Nonholonomic Hamilton-Jacobi equation and Integrability will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-725549