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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.10925 |
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| _version_ | 1866912135702904832 |
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| author | Lee, Chung-Ru |
| author_facet | Lee, Chung-Ru |
| contents | In this paper, we study the determination of Hamiltonian from a given equations of motion. It can be cast into a problem of matrix factorization after reinterpretation of the system as first-order evolutionary equations in the phase space coordinates. We state the criterion on the evolution matrix for a Hamiltonian to exist. In addition, the proof is constructive and an explicit Hamiltonian with accompanied symplectic structure can be obtained. As an application, we will study a few classes of dynamical systems for illustration. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_10925 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Determination of the Hamiltonian from the Equations of Motion with Illustration from Examples Lee, Chung-Ru Mathematical Physics Exactly Solvable and Integrable Systems In this paper, we study the determination of Hamiltonian from a given equations of motion. It can be cast into a problem of matrix factorization after reinterpretation of the system as first-order evolutionary equations in the phase space coordinates. We state the criterion on the evolution matrix for a Hamiltonian to exist. In addition, the proof is constructive and an explicit Hamiltonian with accompanied symplectic structure can be obtained. As an application, we will study a few classes of dynamical systems for illustration. |
| title | Determination of the Hamiltonian from the Equations of Motion with Illustration from Examples |
| topic | Mathematical Physics Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2406.10925 |