Delay ordinary differential equations: from Lagrangian approach to Hamiltonian approach
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914948105371648 |
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| author | Dorodnitsyn, Vladimir Kozlov, Roman Meleshko, Sergey |
| author_facet | Dorodnitsyn, Vladimir Kozlov, Roman Meleshko, Sergey |
| contents | The paper suggests a Hamiltonian formulation for delay ordinary differential equations (DODEs). Such equations are related to DODEs with a Lagrangian formulation via a delay analog of the Legendre transformation. The Hamiltonian delay operator identity is established. It states the relationship for the invariance of a delay Hamiltonian functional, appropriate delay variational equations, and their conserved quantities. The identity is used to formulate a Noether-type theorem, which provides first integrals for Hamiltonian DODEs with symmetries. The relationship between the invariance of the delay Hamiltonian functional and the invariance of the delay variational equations is also examined. Several examples illustrate the theoretical results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_08165 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Delay ordinary differential equations: from Lagrangian approach to Hamiltonian approach Dorodnitsyn, Vladimir Kozlov, Roman Meleshko, Sergey Mathematical Physics Exactly Solvable and Integrable Systems The paper suggests a Hamiltonian formulation for delay ordinary differential equations (DODEs). Such equations are related to DODEs with a Lagrangian formulation via a delay analog of the Legendre transformation. The Hamiltonian delay operator identity is established. It states the relationship for the invariance of a delay Hamiltonian functional, appropriate delay variational equations, and their conserved quantities. The identity is used to formulate a Noether-type theorem, which provides first integrals for Hamiltonian DODEs with symmetries. The relationship between the invariance of the delay Hamiltonian functional and the invariance of the delay variational equations is also examined. Several examples illustrate the theoretical results. |
| title | Delay ordinary differential equations: from Lagrangian approach to Hamiltonian approach |
| topic | Mathematical Physics Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2409.08165 |