Jacobi zeta function and action-angle coordinates for the pendulum

Alain J. Brizard

doi:10.1016/j.cnsns.2012.08.023

Jacobi zeta function and action-angle coordinates for the pendulum

2013-03-01

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Alain J. Brizard *

DOI：10.1016/j.cnsns.2012.08.023

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The Jacobi elliptic functions and integrals play a defining role in analytically describing the motion of the planar pendulum. In the present paper, the Jacobi zeta function is given the physical interpretation as the generating function of the canonical transformation from the pendulum coordinates v and p partial derivative v/partial derivative t to the action-angle coordinates (J, zeta) for both the librating pendulum and the rotating pendulum. (C) 2012 Elsevier B.V. All rights reserved.

Keyword:

Planar pendulum

Jacobi elliptic functions

Action-angle coordinates

Generating function for canonical transformation

Jacobi zeta function and action-angle coordinates for the pendulum

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