The generating function for the canonical transformation from the parallelcanonical coordinates $(p_{\|},s)$ to the action-angle coordinates $(J,\zeta)$for trapped/passing guiding-center orbits in axisymmetric tokamak geometry ispresented. Drawing on the analogy between the phase-space portraits of thelibrating/rotating pendulum and the trapped/passing guiding-center orbits, thegenerating function is expressed in terms of the Jacobi zeta function, whichcan then readily be used to obtain an explicit expression for the bounce-centertransformation for trapped/passing-particles in axisymmetric tokamak geometry.
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