Hamiltonian systems in the vicinity of an equilibrium solution. I - Periodic orbits in resonant cases

Details Hamiltonian systems in the vicinity of an equilibrium solution. I - Periodic orbits in resonant cases Hamiltonian systems in the vicinity of an equilibrium solution. I - Periodic orbits in resonant cases

Mar 1984

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1984cemec..32..231s&link_type=abstract

Celestial Mechanics (ISSN 0008-8714), vol. 32, March 1984, p. 231-246. In French.

Physics

2

Celestial Mechanics, Hamiltonian Functions, Orbital Mechanics, Asymptotic Methods, Equations Of Motion, Galaxies, Linear Systems, Resonance

Scientific paper

The author studies the periodic solutions of an Hamiltonian system with n degrees of freedom, near an equilibrium point, in the vicinity of the resonances ωi/ωj ≅ Ni/Nj. Ni/Nj are fractions in their lowest terms for any pair (i, j). In this case, a general procedure to find the families of periodic solutions is given. The asymptotic solutions can explicitly be calculated including the periods. An application to a galactic dynamics problem in a system with three degrees of freedom near the resonances 2:2:1, is analytically treated in detail.

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