Contact Hamiltonian Mechanics

TL;DR

This paper introduces contact Hamiltonian mechanics, extending symplectic Hamiltonian mechanics to better describe both non-dissipative and dissipative systems through a geometric framework.

Contribution

It develops the theory of contact Hamiltonian mechanics as a natural extension of symplectic mechanics for dissipative systems.

Findings

Generalization of symplectic features to contact case

Framework applicable to dissipative systems

Provides geometric description of non-dissipative and dissipative dynamics

Abstract

In this work we introduce contact Hamiltonian mechanics, an extension of symplectic Hamiltonian mechanics, and show that it is a natural candidate for a geometric description of non-dissipative and dissipative systems. For this purpose we review in detail the major features of standard symplectic Hamiltonian dynamics and show that all of them can be generalized to the contact case.