A Time-Reversible Variable-Stepsize Integrator for Constrained Dynamics

This article considers the design and implementation of variable-timestep methods for simulating holonomically constrained mechanical systems. Symplectic variable stepsizes are briefly discussed, we then consider time-reparameterization techniques employing a time-reversible (symmetric) integration method to solve the equations of motion. We give several numerical examples, including a simulation of an elastic (inextensible, unshearable) rod undergoing large deformations and collisions with the sides of a bounding box. Numerical experiments indicate that adaptive stepping can significantly smooth the numerical energy and improve the overall efficiency of the simulation.