A method for obtaining Hamiltonians with simple periodic solutions

Details A method for obtaining Hamiltonians with simple periodic solutions A method for obtaining Hamiltonians with simple periodic solutions

Mar 1986

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1986aj.....91..660c&link_type=abstract

Astronomical Journal (ISSN 0004-6256), vol. 91, March 1986, p. 660-664.

Statistics

Applications

1

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

Scientific paper

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 = ω1/ω2 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.

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