A note on the application of the von Zeipel method to degenerate Hamiltonians

Through the introduction of a term at each order of the generating function dependent only on the long-period variables, a technique is shown whereby both short- and long-period variables in a degenerate Hamiltonian can be eliminated simultaneously in one transformation with the von Zeipel method, rather than the traditionally separate transformations. The technique is applied to the lunar theory as an example.