Geometric Hamilton-Jacobi theory for systems with external forces
Mathematical Physics
2022-04-14 v2 math.MP
Symplectic Geometry
Classical Physics
Abstract
In this paper, we develop a Hamilton-Jacobi theory for forced Hamiltonian and Lagrangian systems. We study the complete solutions, particularize for Rayleigh systems and present some examples. Additionally, we present a method for the reduction and reconstruction of the Hamilton-Jacobi problem for forced Hamiltonian systems with symmetry. Furthermore, we consider the reduction of the Hamilton-Jacobi problem for a \v{C}aplygin system to the Hamilton-Jacobi problem for a forced Lagrangian system.
Cite
@article{arxiv.2109.13802,
title = {Geometric Hamilton-Jacobi theory for systems with external forces},
author = {Manuel de León and Manuel Lainz and Asier López-Gordón},
journal= {arXiv preprint arXiv:2109.13802},
year = {2022}
}
Comments
39 pages, submitted to J. Math. Phys