Hamilton–Jacobi theory and integrability for autonomous and non-autonomous contact systems

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 May 2023Embargo end date: 01 Jan 2022 Spain, Spain English Publisher:Elsevier BVJournal:Journal of Geometry and Physics, volume 187, page 104,787 (issn: 0393-0440,

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

doi: 10.1016/j.geomphys.2023.104787 , 10.48550/arxiv.2208.07436

arXiv: 2208.07436

handle: 10261/347038

Hamilton–Jacobi theory and integrability for autonomous and non-autonomous contact systems

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Abstract

In this paper, we study the integrability of contact Hamiltonian systems, both time-dependent and independent. In order to do so, we construct a Hamilton--Jacobi theory for these systems following two approaches, obtaining two different Hamilton--Jacobi equations. Compared to conservative Hamiltonian systems, contact Hamiltonian systems depend of one additional parameter. The fact of obtaining two equations reflects whether we are looking for solutions depending on this additional parameter or not. In order to illustrate the theory developed in this paper, we study three examples: the free particle with a linear external force, the freely falling particle with linear dissipation and the damped and forced harmonic oscillator.

27 pages

Countries

Spain, Spain

Related Organizations

Universidad Internacional De La Rioja
Spain
Institute of Mathematical Sciences
Spain
Universidad Internacional de La Rioja (UNIR)
Spain
Spanish National Research Council
Spain

Keywords

37J55, 70H20, 70H33, 53D10, 53Z05, FOS: Physical sciences, Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction for problems in Hamiltonian and Lagrangian mechanics, Problems involving a system of particles with friction, Integrability, Hamilton-Jacobi equations in mechanics, integrability, Complete solutions, Applications of differential geometry to physics, Hamilton–Jacobi equation, FOS: Mathematics, Contact manifolds (general theory), Mathematical Physics, Contact systems, Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests, Mathematical Physics (math-ph), Hamilton-Jacobi equation, complete solutions, Contact Hamiltonian systems, Mathematics - Mathematical Physics, contact Hamiltonian systems, Mathematics - Symplectic Geometry, Symplectic Geometry (math.SG)

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