Analytical investigation of the orbital structure close to the 1:1:1 resonance in spheroidal galaxies
Astronomical Observatory of A. Mickiewicz University, Słoneczna 36, 60-286 Poznań, Poland e-mail: [breiter;iwona]@amu.edu.pl
2 Grupo de Mecánica Espacial, Universidad de Zaragoza, 50009 Zaragoza, Spain e-mail: firstname.lastname@example.org
Accepted: 18 October 2004
The motion of stars in prolate and oblate spheroidal galaxies is studied. Using a combination of Lissajous and Poincaré transformations, we introduce the set of action-angle-like variables. Then, we perturb the problem of the 1:1:1 resonance motion in a spherical, homogenous galaxy, assuming the perturbing potential in the polynomial Ferrers form. We find the orbits that are periodic with respect to the radial and vertical oscillations by inspecting the equilibria of a normalized system. Imposing additional constraints, we find orbits that are periodic in all three coordinates with respect to the system that rotates with a galaxy.
Key words: celestial mechanics / methods: analytical / galaxies: kinematics and dynamics
© ESO, 2005