Geometric Hamilton–Jacobi theory for systems with external forces

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Feb 2022Embargo end date: 01 Jan 2021 Spain English Publisher:AIP PublishingJournal:Journal of Mathematical Physics, volume 63 (issn: 0022-2488, eissn: 1089-7658,

Copyright policy )

Authors: Manuel de León; Manuel Lainz; Asier López-Gordón;

doi: 10.1063/5.0073214 , 10.48550/arxiv.2109.13802

arXiv: 2109.13802

handle: 10016/37366 , 10261/272915

Geometric Hamilton–Jacobi theory for systems with external forces

- Summary
- Subjects
- Metrics

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 Čaplygin system to the Hamilton–Jacobi problem for a forced Lagrangian system.

Country

Spain

Related Organizations

Spanish National Research Council
Spain
Institute of Mathematical Sciences
Spain

Keywords

Geometrical methods, Friction, Matemáticas, 70H20, 70H33, 70F40, 53Z05, Lagrangian mechanics, FOS: Physical sciences, Physics - Classical Physics, Hamilton-Jacobi equations in mechanics, Dynamical systems, FOS: Mathematics, Hamilton-jacobi equations, Differential geometry, Geometric mechanics, Mathematical Physics, Nonholonomic systems related to the dynamics of a system of particles, Física, Classical Physics (physics.class-ph), Mathematical Physics (math-ph), Differentiable manifold, Lagrangian formalism and Hamiltonian formalism in mechanics of particles and systems, Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics, Mathematics - Symplectic Geometry, Hamiltonian mechanics, Symplectic Geometry (math.SG), Hamilton-Jacobi equations, Nonholonomic dynamical systems

Impact byBIP!

	selected citations These citations are derived from selected sources. This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	9
	popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.	Top 10%
	influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	Average
	impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.	Top 10%