First integrals of some two-dimensional integrable Hamiltonian systems
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866917894469713920 |
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| author | Ghosh, Aritra Sinha, Akash Bagchi, Bijan |
| author_facet | Ghosh, Aritra Sinha, Akash Bagchi, Bijan |
| contents | In this paper, we discuss some results on integrable Hamiltonian systems with two degrees of freedom. We revisit the much-studied problem of the two-dimensional harmonic oscillator and discuss its (super)integrability in the light of a canonical transformation which can map the anisotropic oscillator to a corresponding isotropic one. Following this, we discuss the computation of first integrals for integrable two-dimensional systems using the framework of the Jacobi last multiplier. Using the latter, we describe some novel physical examples, namely, the classical Landau problem with a scalar-potential-induced hyperbolic mode, the two-dimensional Kepler problem, and a problem involving a linear curl force. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_19116 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | First integrals of some two-dimensional integrable Hamiltonian systems Ghosh, Aritra Sinha, Akash Bagchi, Bijan Exactly Solvable and Integrable Systems Mathematical Physics Classical Physics In this paper, we discuss some results on integrable Hamiltonian systems with two degrees of freedom. We revisit the much-studied problem of the two-dimensional harmonic oscillator and discuss its (super)integrability in the light of a canonical transformation which can map the anisotropic oscillator to a corresponding isotropic one. Following this, we discuss the computation of first integrals for integrable two-dimensional systems using the framework of the Jacobi last multiplier. Using the latter, we describe some novel physical examples, namely, the classical Landau problem with a scalar-potential-induced hyperbolic mode, the two-dimensional Kepler problem, and a problem involving a linear curl force. |
| title | First integrals of some two-dimensional integrable Hamiltonian systems |
| topic | Exactly Solvable and Integrable Systems Mathematical Physics Classical Physics |
| url | https://arxiv.org/abs/2409.19116 |