Action-angle coordinates of spherical pendulums with symmetric quadratic potentials

Fuente: arXiv
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Main Authors: Peng, Chengle, Tang, Xiudi
Format: Preprint
Published: 2025
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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