Journal
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
Volume 18, Issue 3, Pages 511-518Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.cnsns.2012.08.023
Keywords
Planar pendulum; Jacobi elliptic functions; Action-angle coordinates; Generating function for canonical transformation
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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.
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