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arXiv · 2509.04207

Action-angle coordinates of spherical pendulums with symmetric quadratic potentials

Chengle Peng·Xiudi Tang
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Abstract

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.

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Chengle Peng, Xiudi Tang. 2025-09-04. Action-angle coordinates of spherical pendulums with symmetric quadratic potentials. https://arxiv.org/abs/2509.04207

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