Nonsmooth Herglotz variational principle
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866929402755940352 |
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| author | López-Gordón, Asier Colombo, Leonardo de León, Manuel |
| author_facet | López-Gordón, Asier Colombo, Leonardo de León, Manuel |
| contents | In this paper, the theory of smooth action-dependent Lagrangian mechanics (also known as contact Lagrangians) is extended to a non-smooth context appropriate for collision problems. In particular, we develop a Herglotz variational principle for non-smooth action-dependent Lagrangians which leads to the preservation of energy and momentum at impacts. By defining appropriately a Legendre transform, we can obtain the Hamilton equations of motion for the corresponding non-smooth Hamiltonian system. We apply the result to a billiard problem in the presence of dissipation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_02033 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Nonsmooth Herglotz variational principle López-Gordón, Asier Colombo, Leonardo de León, Manuel Optimization and Control Systems and Control Mathematical Physics 53Z05, 70F35, 70F40, 93C30 In this paper, the theory of smooth action-dependent Lagrangian mechanics (also known as contact Lagrangians) is extended to a non-smooth context appropriate for collision problems. In particular, we develop a Herglotz variational principle for non-smooth action-dependent Lagrangians which leads to the preservation of energy and momentum at impacts. By defining appropriately a Legendre transform, we can obtain the Hamilton equations of motion for the corresponding non-smooth Hamiltonian system. We apply the result to a billiard problem in the presence of dissipation. |
| title | Nonsmooth Herglotz variational principle |
| topic | Optimization and Control Systems and Control Mathematical Physics 53Z05, 70F35, 70F40, 93C30 |
| url | https://arxiv.org/abs/2208.02033 |