Periodic Poincare solutions for a canonical system with one degree of freedom

Details Periodic Poincare solutions for a canonical system with one degree of freedom Periodic Poincare solutions for a canonical system with one degree of freedom

Aug 1985

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1985sval...11..267m&link_type=abstract

(Pis'ma v Astronomicheskii Zhurnal, vol. 11, Aug. 1985, p. 634-639) Soviet Astronomy Letters (ISSN 0360-0327), vol. 11, July-Aug

Mathematics

1

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

Scientific paper

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 time-periodic disturbing part. Poincare's method is used to demonstrate that the perturbed system has periodic solutions, and Liapunov-stability 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 three-body problem.

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