Numerical Integrators for Mechanical Systems on Lie Groups
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915291750989824 |
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| author | Vivek, Viyom de Diego, David Martin Banavar, Ravi N |
| author_facet | Vivek, Viyom de Diego, David Martin Banavar, Ravi N |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_12103 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Numerical Integrators for Mechanical Systems on Lie Groups Vivek, Viyom de Diego, David Martin Banavar, Ravi N Numerical Analysis Differential Geometry 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. |
| title | Numerical Integrators for Mechanical Systems on Lie Groups |
| topic | Numerical Analysis Differential Geometry |
| url | https://arxiv.org/abs/2505.12103 |