Invariants to All Orders in Classical Perturbation Theory

  title={Invariants to All Orders in Classical Perturbation Theory},
  author={Timothy Patrick Coffey},
The method of averaging is applied to systems having Hamiltonians of the form H=H0(J)+eH1(J,ψ,p,q), where H1 is periodic in each of the components of Ψ. When the system is nondegenerate it is shown that corresponding to each component of Ψ there is a quantity Ki which is invariant to all orders in e. When the system has an m‐fold degeneracy, somewhat weaker results are obtained. In this case it is shown that the Hamiltonian, when expressed in terms of the average variables, depends on the angle… CONTINUE READING