On particular integrability for (co)symplectic and (co)contact Hamiltonian systems
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2023
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866910568422572032 |
|---|---|
| author | Azuaje, R. Escobar-Ruiz, A. M. |
| author_facet | Azuaje, R. Escobar-Ruiz, A. M. |
| contents | As a generalization and extension of our previous paper [Escobar-Ruiz and Azuaje, J. Phys. A: Math. Theor. 57, 105202 (2024)], in this work, the notions of particular integral and particular integrability in classical mechanics are extended to the formalisms of cosymplectic, contact and cocontact geometries. This represents a natural scheme to study nonintegrable time-dependent systems where only a part of the whole dynamics satisfies the conditions for integrability. Specifically, for Hamiltonian systems on cosymplectic, contact and cocontact manifolds, it is demonstrated that the existence of a particular integral allows us to f ind certain integral curves from a reduced, lower dimensional, set of Hamilton equations. In the case of particular integrability, these trajectories can be obtained by quadratures. Notably, for dissipative systems described by contact geometry, a particular integral can be viewed as a generalization of the important concept of dissipated quantity as well. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_17356 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On particular integrability for (co)symplectic and (co)contact Hamiltonian systems Azuaje, R. Escobar-Ruiz, A. M. Mathematical Physics As a generalization and extension of our previous paper [Escobar-Ruiz and Azuaje, J. Phys. A: Math. Theor. 57, 105202 (2024)], in this work, the notions of particular integral and particular integrability in classical mechanics are extended to the formalisms of cosymplectic, contact and cocontact geometries. This represents a natural scheme to study nonintegrable time-dependent systems where only a part of the whole dynamics satisfies the conditions for integrability. Specifically, for Hamiltonian systems on cosymplectic, contact and cocontact manifolds, it is demonstrated that the existence of a particular integral allows us to f ind certain integral curves from a reduced, lower dimensional, set of Hamilton equations. In the case of particular integrability, these trajectories can be obtained by quadratures. Notably, for dissipative systems described by contact geometry, a particular integral can be viewed as a generalization of the important concept of dissipated quantity as well. |
| title | On particular integrability for (co)symplectic and (co)contact Hamiltonian systems |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2309.17356 |