Geometric Hamilton-Jacobi theory for systems with external forces Articles uri icon

authors

  • LEON RODRIGUEZ, MANUEL DE
  • LAINZ VALCAZAR, MANUEL
  • LOPEZ GORDON, ASIER

publication date

  • February 2022

start page

  • 022901-1

end page

  • 022901-26

issue

  • 2

volume

  • 63

International Standard Serial Number (ISSN)

  • 0022-2488

Electronic International Standard Serial Number (EISSN)

  • 1089-7658

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 Caplygin system to the Hamilton-Jacobi problem for a forced Lagrangian system.

subjects

  • Mathematics
  • Physics

keywords

  • friction; hamilton-jacobi equations; hamiltonian mechanics; lagrangian mechanics; differentiable manifold; differential geometry; geometric mechanics; geometrical methods; dynamical systems