Symplectic Schemes for Birkhoffian System

TL;DR

This paper develops symplectic schemes for Birkhoffian systems, a generalization of Hamiltonian mechanics, ensuring structure-preserving numerical integration for nonconservative systems.

Contribution

It introduces a method to construct symplectic schemes for Birkhoffian systems using generating functions, extending symplectic integrators to nonconservative dynamics.

Findings

Symplectic structure of Birkhoffian systems is established.

Symplecticity of Birkhoffian phase flow is demonstrated.

A generating function method for symplectic schemes is proposed.

Abstract

A universal symplectic structure for a Newtonian system including nonconservative cases can be constructed in the framework of Birkhoffian generalization of Hamiltonian mechanics. In this paper the symplectic geometry structure of Birkhoffian system is discussed, then the symplecticity of Birkhoffian phase flow is presented. Based on these properties we give a way to construct symplectic schemes for Birkhoffian system by using the generating function method.