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. © 2010 American Institute of Physics.
Pendulum, elliptic functions, and relative cohomology classes / J. P., Francoise; P. L., Garrido; Gallavotti, Giovanni. - In: JOURNAL OF MATHEMATICAL PHYSICS. - ISSN 0022-2488. - STAMPA. - 51:3(2010), pp. 032901-+12. [10.1063/1.3316076]
Pendulum, elliptic functions, and relative cohomology classes
GALLAVOTTI, Giovanni
2010
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. © 2010 American Institute of Physics.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
