Theory of General Perturbations with Unspecified Canonical Variables

Abstract A theorem by Lie in canonical transformations is applied to the theory of general perturbations. In the present theory (a) all formulas are in the form of canonical invariance so that they are valid for any set of canonical variables, (b) the perturbations of any quantities, regardless of whether they are elements or coordinates, are given by a simple formula and in an explicit form, and (c) the theory is applicable to such cases where the undisturbed portion of Hamiltonian depends on an angular variable as well as momentum variables. The motion of an artificial satellite is discussed as an application of the general theory.