Contact dynamics, contact Poisson bracket, and symplectic integrator -- Even Arnold nodds

TL;DR

This paper introduces a variational formulation of contact dynamics using an integration factor, formulates the contact Poisson bracket and Lagrangian, and develops a hybrid leap-frog symplectic integrator for dissipative systems.

Contribution

It presents a novel variational approach to contact dynamics, formulates the contact Poisson bracket and Lagrangian, and introduces a new symplectic integrator for dissipative systems.

Findings

Derivation of equations of motion via variational principle

Formulation of contact Poisson bracket and Lagrangian

Development of hybrid leap-frog symplectic integrator

Abstract

By introducing an integration factor to the differential one-form of contact dynamics, equations of motion are derived variationally, and contact Poisson bracket and contact Lagrangian are formulated. Discrete symplectic integrator, named hybrid leap-frog method, is found to be a numerical solver of equations of motion for contact dissipative systems.