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