A&A 431, 1145-1155 (2005)
Analytical investigation of the orbital structure close to the 1:1:1 resonance in spheroidal galaxiesS. Breiter1, A. Elipe2 and I. Wytrzyszczak1
1 Astronomical Observatory of A. Mickiewicz University, Sloneczna 36, 60-286 Poznan, Poland
2 Grupo de Mecánica Espacial, Universidad de Zaragoza, 50009 Zaragoza, Spain
(Recieved 2 July 2004 / 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