Infinitesimal symmetries in Contact Hamiltonian systems
Mathematical Physics
2020-04-22 v2 Differential Geometry
Dynamical Systems
math.MP
Symplectic Geometry
Abstract
In this paper, we extend the well-known Noether theorem for Lagrangian systems to contact Lagrangian systems. We introduce a classification of infinitesimal symmetries and obtain the corresponding dissipated quantities. We notice that in contact dynamics, the existence of infinitesimal symmetries does not produce conserved quantities, but functions that dissipate at the same rate than the energy; so, the corresponding quotients are true conserved quantities.
Cite
@article{arxiv.1909.07892,
title = {Infinitesimal symmetries in Contact Hamiltonian systems},
author = {Manuel de León and Manuel Lainz Valcázar},
journal= {arXiv preprint arXiv:1909.07892},
year = {2020}
}