TIME-DEPENDENT NORMAL-FORM HAMILTONIAN FOR DYNAMICAL EQUILIBRIA

A new time-dependent normal-form procedure for dynamical equilibria (u ndergoing parametric excitation) of one-dimensional (1D) Hamiltonian s ystems is developed with the method of Lie transforms. The expansion i s based on the Lewis invariant for the linearized motion. The time-dep endent Hamiltonian normal form reduces smoothly to the usual represent ation in the autonomous limit. Illustrative examples of the formalism are focused on time-periodic systems and the dynamics of Hamiltonian s witching.