Homogeneous potentials, Lagrange's identity and Poisson geometry
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910083240165376 |
|---|---|
| author | Tsiganov, A. V. |
| author_facet | Tsiganov, A. V. |
| contents | The Lagrange identity expresses the second derivative of the moment of inertia of a system of material points through kinetic energy and homogeneous potential energy, from which follows the Jacobi well-known result on the instability of a system of gravitating bodies. In this work, it is proven that if a Hamiltonian system satisfies the Lagrange identity, then it possesses additional tensor invariants that are not expressed through the basic invariants existing for all Hamiltonian systems. A new class of Hamiltonian systems with inhomogeneous potentials is considered, which also possess similar additional tensor invariants. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_19903 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Homogeneous potentials, Lagrange's identity and Poisson geometry Tsiganov, A. V. Exactly Solvable and Integrable Systems Mathematical Physics Dynamical Systems Symplectic Geometry The Lagrange identity expresses the second derivative of the moment of inertia of a system of material points through kinetic energy and homogeneous potential energy, from which follows the Jacobi well-known result on the instability of a system of gravitating bodies. In this work, it is proven that if a Hamiltonian system satisfies the Lagrange identity, then it possesses additional tensor invariants that are not expressed through the basic invariants existing for all Hamiltonian systems. A new class of Hamiltonian systems with inhomogeneous potentials is considered, which also possess similar additional tensor invariants. |
| title | Homogeneous potentials, Lagrange's identity and Poisson geometry |
| topic | Exactly Solvable and Integrable Systems Mathematical Physics Dynamical Systems Symplectic Geometry |
| url | https://arxiv.org/abs/2511.19903 |