Jacobi last multiplier and two-dimensional superintegrable oscillators
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909260303040512 |
|---|---|
| author | Sinha, Akash Ghosh, Aritra |
| author_facet | Sinha, Akash Ghosh, Aritra |
| contents | In this paper, we examine the role of the Jacobi last multiplier in the context of two-dimensional oscillators. We first consider two-dimensional unit-mass oscillators admitting a separable Hamiltonian description, i.e., $H = H_1 + H_2$, where $H_1$ and $H_2$ are the Hamiltonians of two one-dimensional unit-mass oscillators; it is shown that there exists a third functionally-independent first integral $Θ$, thereby ensuring superintegrablility. Various examples are explicitly worked out. We then consider position-dependent-mass oscillators and the Bateman pair, where the latter consists of a pair of dissipative linear oscillators. Quite remarkably, the Bateman pair is found to be superintegrable, despite admitting a Hamiltonian which cannot be separated into those of two isolated (non-interacting) one-dimensional oscillators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_08837 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Jacobi last multiplier and two-dimensional superintegrable oscillators Sinha, Akash Ghosh, Aritra Exactly Solvable and Integrable Systems Mathematical Physics Classical Physics In this paper, we examine the role of the Jacobi last multiplier in the context of two-dimensional oscillators. We first consider two-dimensional unit-mass oscillators admitting a separable Hamiltonian description, i.e., $H = H_1 + H_2$, where $H_1$ and $H_2$ are the Hamiltonians of two one-dimensional unit-mass oscillators; it is shown that there exists a third functionally-independent first integral $Θ$, thereby ensuring superintegrablility. Various examples are explicitly worked out. We then consider position-dependent-mass oscillators and the Bateman pair, where the latter consists of a pair of dissipative linear oscillators. Quite remarkably, the Bateman pair is found to be superintegrable, despite admitting a Hamiltonian which cannot be separated into those of two isolated (non-interacting) one-dimensional oscillators. |
| title | Jacobi last multiplier and two-dimensional superintegrable oscillators |
| topic | Exactly Solvable and Integrable Systems Mathematical Physics Classical Physics |
| url | https://arxiv.org/abs/2306.08837 |