Dynamical behaviour and structure of the optical variational integrators towards degenerate lagrangian systems

Variational integrators (VI) for degenerate lagrangian systems (DLS) are prone to parasitic instabilities. In this paper, the VI for DLS is written as general linear methods (GLM) and the corresponding parasitic growth parameters are calculated. Then, to counteract the consequences of parasitism, GLM is projected onto the target manifold using the conventional projection technique, which numerically preserves the invariants of the degenerate Lagrangian systems. This allows us to study the different attributes of the variational integrators in different circumstances which play a paramount part in numerically preserving the qualitative features of the dynamics for a long-time. Our focus is on preserving the system’s global properties rather than minimizing local errors. The preservation of geometric properties is advantageous for stability and crucial for long-time simulations as it bounds global error growth and reduces numerical artifacts.