Variational integrators and time-dependent lagrangian systems

TL;DR

This paper introduces a method for creating variational integrators tailored for time-dependent Lagrangian systems, ensuring symplecticity, momentum preservation, and accurate energy variation tracking.

Contribution

It develops a novel approach to construct variational integrators that handle time-dependent Lagrangian systems while maintaining key geometric properties.

Findings

Algorithms are symplectic and preserve momentum maps.

The integrators accurately describe energy variation.

The method extends variational integrators to time-dependent systems.

Abstract

This paper presents a method to construct variational integrators for time-dependent lagrangian systems. The resulting algorithms are symplectic, preserve the momentum map associated with a Lie group of symmetries and also describe the energy variation.