NDLI: Linear Almost Poisson Structures and Hamilton-jacobi Equation. Applications to Nonholonomic Mechanics

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Linear Almost Poisson Structures and Hamilton-jacobi Equation. Applications to Nonholonomic Mechanics

Content Provider	Semantic Scholar
Author	León, Manuel De Marrero, Juan C. Diego, David Martín De
Abstract	In this paper, we study the underlying geometry in the classical Hamilton-Jacobi equation. The proposed formalism is also valid for nonholonomic systems. We first introduce the essential geometric ingredients: a vector bundle, a linear almost Poisson structure and a Hamiltonian function, both on the dual bundle (a Hamiltonian system). From them, it is possible to formulate the Hamilton-Jacobi equation, obtaining as a particular case, the classical theory. The main application in this paper is to nonholonomic mechanical systems. For it, we first construct the linear almost Poisson structure on the dual space of the vector bundle of admissible directions, and then, apply the Hamilton-Jacobi theorem. Another important fact in our paper is the introduction of the notion of morphisms preserving the Hamiltonian system; indeed, this concept will be very useful to treat with reduction procedures for systems with symmetries. Several detailed examples are given to illustrate the utility of these new developments.
File Format	PDF HTM / HTML
Alternate Webpage(s)	http://arxiv.org/pdf/0801.4358v2.pdf
Language	English
Access Restriction	Open
Subject Keyword	Appendix Bellman equation Calculus of variations Control system Dual Formal grammar Formal system Hamilton–Jacobi–Bellman equation Jacobi eigenvalue algorithm Jacobi method Local coordinates Mechanics Numerical analysis Optimal control Subgroup Theory
Content Type	Text
Resource Type	Article

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