A method for obtaining Hamiltonians with simple periodic solutions
Abstract
The authors present a method for obtaining Hamiltonian systems with accurate periodic solutions. The general solution of a degenerate integrable Hamiltonian is expressed in a polynomial form when the ratio of the frequencies q = ω_{1}/ω_{2} is an integer, or as a power series when q is a rational number. Adding this expression as a perturbation in the above Hamiltonian, a new nontrivial Hamiltonian with one exact periodic solution is obtained. Some possible applications of these findings are also discussed.
 Publication:

The Astronomical Journal
 Pub Date:
 March 1986
 DOI:
 10.1086/114049
 Bibcode:
 1986AJ.....91..660C
 Keywords:

 Celestial Mechanics;
 Hamiltonian Functions;
 Periodic Functions;
 Stellar Orbits;
 Astrodynamics;
 Elliptical Orbits;
 Orbit Perturbation;
 Polynomials;
 Power Series;
 Astrophysics