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Pendulum, Elliptic Functions and Relative Cohomology Classes

FM 09-09, Journal of Mathematical Physics, 51, 032901 (2010); doi: 10.1063/1.3316076

*Authors* J.P. Francoise, P.L. Garrido, G.Gallavotti

*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.

G.Gallavotti
Last modified: Thu Sep 17 11:39:50 CEST 2009