English

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.

Keywords

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

R2 v1 2026-06-24T06:26:37.928Z