Variational Principles for Hamiltonian Systems
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866908307699007488 |
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| author | Tran, Brian K. Leok, Melvin |
| author_facet | Tran, Brian K. Leok, Melvin |
| contents | Motivated by recent developments in Hamiltonian variational principles, Hamiltonian variational integrators, and their applications such as to optimization and control, we present a new Type II variational approach for Hamiltonian systems, based on a virtual work principle that enforces the Type II boundary conditions through a combination of essential and natural boundary conditions; particularly, this approach allows us to define this variational principle intrinsically on manifolds. We first develop this variational principle on vector spaces and subsequently extend it to parallelizable manifolds, general manifolds, as well as to the infinite-dimensional setting. Furthermore, we provide a review of variational principles for Hamiltonian systems in various settings as well as their applications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_02960 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Variational Principles for Hamiltonian Systems Tran, Brian K. Leok, Melvin Symplectic Geometry Mathematical Physics 37J06, 37K06 Motivated by recent developments in Hamiltonian variational principles, Hamiltonian variational integrators, and their applications such as to optimization and control, we present a new Type II variational approach for Hamiltonian systems, based on a virtual work principle that enforces the Type II boundary conditions through a combination of essential and natural boundary conditions; particularly, this approach allows us to define this variational principle intrinsically on manifolds. We first develop this variational principle on vector spaces and subsequently extend it to parallelizable manifolds, general manifolds, as well as to the infinite-dimensional setting. Furthermore, we provide a review of variational principles for Hamiltonian systems in various settings as well as their applications. |
| title | Variational Principles for Hamiltonian Systems |
| topic | Symplectic Geometry Mathematical Physics 37J06, 37K06 |
| url | https://arxiv.org/abs/2410.02960 |