Resumen de Variational symmetries in the Hamiltonian formalism (5 pages)

Gerardo Francisco Torres del Castillo

• We consider the effect on the Hamilton equations of an arbitrary coordinate transformation in the extended configuration space, $q_{i}' = q_{i}'(q_{j}, t)$, $t' = t'(q_{j}, t)$ (which may not be canonical) and we show that when the Hamiltonian is invariant under a one-parameter family of these transformations, there is an associated nontrivial constant of motion.