Action-angle coordinates for the pendulum problem

Details Action-angle coordinates for the pendulum problem Action-angle coordinates for the pendulum problem

2011-08-25

arxiv.org/abs/1108.4970v2

Physics

Classical Physics

5 pages and 1 figure. Revised manuscript provides a more concise treatment of partial derivatives at constant action and const

Scientific paper

The action-angle coordinates for the planar pendulum problem are expressed in terms of the Jacobi elliptic functions and integrals. In particular, we show that the Jacobi zeta function generates the canonical transformation from the pendulum coordinates $\vartheta$ and $p \equiv \partial\vartheta/\partial t$ to the action-angle coordinates $(J,\zeta)$ for both the librating pendulum and the rotating pendulum.

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