Action-angle coordinates of spherical pendulums with symmetric quadratic potentials
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912691067551744 |
|---|---|
| author | Peng, Chengle Tang, Xiudi |
| author_facet | Peng, Chengle Tang, Xiudi |
| contents | We study the spherical pendulum system with an arbitrary potential function $V = V (z)$, which is an integrable system with a first integral whose Hamiltonian flow is periodic. We give an explicit solution to this integrable system and then we compute its action-angle coordinates. In the special case where the potential function is symmetric quadratic like $V = z^2$, we represent its action-angle coordinates in terms of elliptic integrals, and calculate the monodromy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_04207 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Action-angle coordinates of spherical pendulums with symmetric quadratic potentials Peng, Chengle Tang, Xiudi Symplectic Geometry 53D20, 70H06 We study the spherical pendulum system with an arbitrary potential function $V = V (z)$, which is an integrable system with a first integral whose Hamiltonian flow is periodic. We give an explicit solution to this integrable system and then we compute its action-angle coordinates. In the special case where the potential function is symmetric quadratic like $V = z^2$, we represent its action-angle coordinates in terms of elliptic integrals, and calculate the monodromy. |
| title | Action-angle coordinates of spherical pendulums with symmetric quadratic potentials |
| topic | Symplectic Geometry 53D20, 70H06 |
| url | https://arxiv.org/abs/2509.04207 |