The interaction representation for classical mechanics starting from an operational formulation of the same is presented. General criteria to be satisfied by a slowly time-dependent Hamiltonian in order to possess adiabatic invariants of the m-th order are given. A general method, based on techniques similar to those used to evaluate timedependent perturbations in quantum mechanics, to calculate the degree of approximate constancy of such adiabatic invariants for Hamiltonians depending slowly but at a finite rate on time is discussed. These methods were applied to the adiabatic invariants that appear in thermonuclear plasma, evaluating the errors made in the guiding center approximation. (auth)