Hamiltonian perturbation theory in noncanonical coordinates

The traditional methods of Hamiltonian perturbation theory in classical mechanics are first presented in a way which clearly displays their differential-geometric foundations. These are then generalized to the case of noncanonical in phase space. In the new method the Hamiltonian H is treated, not as a scalar in phase space, but as one component of the fundamental form p dq−Hdt. The perturbation analysis is applied to this entire form, in all of its components.