Control of Parasitism in Variational Integrators for Degenerate Lagrangian Systems

TL;DR

This paper addresses parasitic growth in variational integrators for degenerate Lagrangian systems by analyzing their linear method representation and applying projection techniques to preserve invariants over long time integrations.

Contribution

It introduces a method to compute parasitic growth parameters and applies a projection technique to improve long-term energy conservation in these systems.

Findings

Parasitic growth parameters can be effectively calculated.

Projection techniques help preserve invariants.

Enhanced long-term stability of variational integrators.

Abstract

This paper deals with the control of parasitism in variational integrators for degenerate Lagrangian systems by writing them as general linear methods. This enables us to calculate their parasitic growth parameters which are responsible for the loss of long-time energy conservation properties of these algorithms. As a remedy and to offset the effects of parasitism, the standard projection technique is then applied to the general linear methods to numerically preserve the invariants of the degenerate Lagrangian systems by projecting the solution onto the desired manifold.