Simple three-dimensional periodic orbits in a galactic-type potential

Details Simple three-dimensional periodic orbits in a galactic-type potential Simple three-dimensional periodic orbits in a galactic-type potential

Dec 1985

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1985cemec..37..387c&link_type=abstract

Celestial Mechanics (ISSN 0008-8714), vol. 37, Dec. 1985, p. 387-414.

Mathematics

48

Celestial Mechanics, Galaxies, Orbits, Branching (Mathematics), Eigenvalues

Scientific paper

The evolution of families of simple periodic orbits in a three-dimensional potential representing three coupled harmonic oscillators, simulating the central regions of a perturbed triaxial elliptical galaxy, is investigated analytically, extending the results of Magnenat (1982) to a double-resonance case. Initial conditions, characteristic curves, existence diagrams, and stability curves are presented for a total of 16 subfamilies. It is shown that stable and simply unstable families produce families with double or complex instability via direct or inverse bifurcations, with some families splitting apart and other joining together. The main families are found to be stable in most cases where the energy is less than the escape energy, although stable orbits exist in some cases with energy four times the escape energy.

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