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Title:
Motion in the core of a triaxial potential
Authors:
de Zeeuw, T.
Affiliation:
AA(Leiden, Rijksuniversiteit, Sterrewacht, Netherlands)
Publication:
Royal Astronomical Society, Monthly Notices (ISSN 0035-8711), vol. 215, Aug. 15, 1985, p. 731-760. CECAM-supported research. (MNRAS Homepage)
Publication Date:
08/1985
Category:
Astrophysics
Origin:
STI
NASA/STI Keywords:
ELLIPTICAL GALAXIES, GRAVITATIONAL FIELDS, STELLAR MOTIONS, STELLAR ORBITS, EIGENVALUES, RESONANCE, SERIES EXPANSION
Bibliographic Code:
1985MNRAS.215..731D

Abstract

The near-harmonic motion in the core of a general triaxial potential is studied by means of the averaging method. The case of a near 1:1:1 resonance between the fundamental orbital frequencies is investigated in detail. It is shown that all orbits possess a second, asymptotic, isolating integral in addition to the energy. In the spherical limit this integral reduces to the square of the angular momentum. The simple periodic orbits are derived, and their stability properties are calculated. There may be up to 14 distinct families of simple periodic orbits, some of which are not in any of the symmetry planes of the potential. For potentials that are nearly spherical, which is the case for the gravitational potentials of elliptical galaxies, an approximate third integral of motion exists. In this case the orbital structure becomes much simpler, and is nearly identical to that in a Staeckel potential, for which the equations of motion separate in ellipsoidal coordinates. The effects of figure rotation on these results are discussed briefly.

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