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arXiv · 2503.19724

Variational Collision Integrators for Nonholonomic Lagrangian Systems

Álvaro Rodríguez Abella·Leonardo Colombo
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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.

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Álvaro Rodríguez Abella, Leonardo Colombo. 2025-03-25. Variational Collision Integrators for Nonholonomic Lagrangian Systems. https://arxiv.org/abs/2503.19724

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