Chaotic and regular motion around generalized Kalnajs discs

TL;DR

This paper investigates the dynamics of test particles around generalized Kalnajs discs, revealing stability characteristics and the coexistence of chaotic and regular motions through analytical and numerical methods.

Contribution

It provides a detailed analysis of orbital stability and chaos in gravitational fields of generalized Kalnajs discs, highlighting the conditions for regular and chaotic motion.

Findings

Radial stability and vertical instability dominate the disc models.

Chaos occurs in disc-crossing orbits, while other orbits are regular.

The study uses Poincare surfaces of section and Lyapunov numbers to characterize motion.

Abstract

The motion of test particles in the gravitational fields generated by the first four members of the infinite family of generalized Kalnajs discs, is studied. In first instance, we analyze the stability of circular orbits under radial and vertical perturbations and describe the behavior of general equatorial orbits and so we find that radial stability and vertical instability dominate such disc models. Then we study bounded axially symmetric orbits by using the Poincare surfaces of section and Lyapunov characteristic numbers and find chaos in the case of disc-crossing orbits and completely regular motion in other cases.