Astronomy and Astrophysics – Astrophysics
Scientific paper
Jul 1986
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1986a%26a...162...45r&link_type=abstract
Astronomy and Astrophysics (ISSN 0004-6361), vol. 162, no. 1-2, July 1986, p. 45-53.
Astronomy and Astrophysics
Astrophysics
4
Elliptical Galaxies, Galactic Structure, Orbit Calculation, Stellar Motions, Amplitudes, Approximation, Lissajous Figures, Periodic Variations, Resonance
Scientific paper
Perturbation techniques are added to Hale's (1963) rigorous equations to obtain a lowest approximation to the periodic orbits in the central region of triaxial systems of elliptical galaxies. A previous model of nearly spherical stellar objects with a 1:1:1 resonance is extended to cover ellipsoidal systems with unequal axes, i.e., nearly-prolate and prolate systems. The triaxial potential of the central region is treated as a three-dimensional harmonic oscillator disturbed by quadratic and quartic terms. The model is used to inventory periodic Lisajous orbits in space and in a symmetry plane; the predictions compare well with exact numerical calculations of the same values. The model is concluded to be useful for preliminary estimates of the shape of the orbits, the various resonances, and links between families of axial, two- and three-dimensional orbits.
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