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arXiv · 2505.12103

Numerical Integrators for Mechanical Systems on Lie Groups

Viyom Vivek·David Martin de Diego·Ravi N Banavar
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Abstract

Retraction maps are known to be the seed for all numerical integrators. These retraction maps-based integrators can be further lifted to tangent and cotangent bundles, giving rise to structure-preserving integrators for mechanical systems. We explore the particular case where the configuration space of our mechanical system is a Lie group with certain symmetries. Here, the integrator simplifies based on the property that the tangent and cotangent bundles of Lie groups are trivializable. Finally, we present a framework for designing numerical integrators for Euler- Poincare and Lie-Poisson type equations.

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Viyom Vivek, David Martin de Diego, Ravi N Banavar. 2025-05-17. Numerical Integrators for Mechanical Systems on Lie Groups. https://arxiv.org/abs/2505.12103

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