
FM 10-00, arxiv:

Jean Pierre Francoise, Pedro L. Garrido, Giovanni Gallavotti

Pendulum, Elliptic Functions and Relative Cohomology Classes

Abstract: Revisiting canonical integration of the classical pendulum
    around its unstable equilibrium, normal hyperbolic canonical
    coordinates are constructed and an identity between elliptic
    functions is found whose proof can be based on symplectic geometry
    and global relative cohomology. Alternatively it can be reduced to
    a well known identity between elliptic functions. Normal canonical
    action-angle variables are also constructed around the stable
    equilibrium and a corresponding identity is exhibited.
