Variational Collision Integrators for Nonholonomic Lagrangian Systems
Dynamical Systems
2025-03-26 v1 Mathematical Physics
math.MP
Abstract
A discrete theory for implicit nonholonomic Lagrangian systems undergoing elastic collisions is developed. It is based on the discrete Lagrange-d'Alembert-Pontryagin variational principle and the dynamical equations thus obtained are the discrete nonholonomic implicit Euler-Lagrange equations together with the discrete conditions for the elastic impact. To illustrate the theory, variational integrators with collisions are built for several examples, including a bouncing ellipse and a nonholonomic spherical pendulum evolving inside a cylinder.
Cite
@article{arxiv.2503.19724,
title = {Variational Collision Integrators for Nonholonomic Lagrangian Systems},
author = {Álvaro Rodríguez Abella and Leonardo Colombo},
journal= {arXiv preprint arXiv:2503.19724},
year = {2025}
}
Comments
4 figures