Periodic Poincare solutions for a canonical system with one degree of freedom
Abstract
Existence criteria are obtained for periodic solutions of an almost integrable canonical system with one degree of freedom. The system Hamiltonian is assumed to be analytic in its arguments, with a timeperiodic disturbing part. Poincare's method is used to demonstrate that the perturbed system has periodic solutions, and Liapunovstability criteria are derived for them. This type of problem arises in various contexts in celestial mechanics: e.g., (1) the problem of the plane periodic motions of a satellite about its center of mass in an elliptical orbit; and (2) the problem of the periodic orbits of a body of negligble mass in the plane restricted threebody problem.
 Publication:

Soviet Astronomy Letters
 Pub Date:
 August 1985
 Bibcode:
 1985SvAL...11..267M
 Keywords:

 Canonical Forms;
 Degrees Of Freedom;
 Perturbation Theory;
 Poincare Problem;
 Hamiltonian Functions;
 Inequalities;
 Liapunov Functions;
 Transformations (Mathematics);
 Physics (General)