Orbits in global and local galactic potentials
Connections between global and local potentials in two galactic models are described. The first model is a logarithmic potential while the second is a four-component mass model. The first model describes plane motion in an elliptical galaxy with a dense nucleus or bulge of radius c, while the second is a composite mass model. Expanding the global potentials in the vicinity of a circular orbit, we find the potential of the corresponding two-dimensional perturbed harmonic oscillator. In the first case, the local potential shows two interesting resonances: the 1:1 and the 4:3 resonances. The appearance of these two cases depends on the flattening parameter of the global potential or the position of the equilibrium point. Expressions connecting the parameters of the global and local potentials are obtained. The second model produces a local potential that can show a large number of resonances depending on the position of the equilibrium point. A relation between the global and local energies of the system is given in both cases.
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