Abstract
We investigate the orbital evolution of a system of N mutually interacting stars on initially circular orbits around the dominating central mass. We include the perturbative influence of a distant axisymmetric source and an extended spherical potential.
In particular, we focus on the case when the secular evolution of orbital eccentricities is suppressed by the spherical perturbation. By means of standard perturbation methods, we derive semi-analytic formulae for the evolution of normal vectors of the individual orbits.
We find its two qualitatively different modes. Either the orbits interact strongly and, under such circumstances, become dynamically coupled, precessing synchronously in the potential of the axisymmetric perturbation, or, if their mutual interaction is weaker, the orbits precess independently, interchanging periodically their angular momentum, which leads to oscillations of inclinations.
We argue that these processes may have been fundamental to the evolution of the disc of young stars orbiting the supermassive black hole in the centre of the Milky Way.