On orbits for a particular case of axial symmetry

Abstract

A particular case of steady state and axial symmetry -the potential formula proposed by Miyamoto and Nagai - is studied. A number of orbits of a bound test particle is determined numerically, with both, the potential parameters and initial conditions, varied. Unlike special cases, such as nearly circular and nearly planar orbits, in the case of 'truly spatial orbits' the time dependence of the coordinates becomes very complicated and a mathematical treatment including any known periodic functions is hardly possible. Bearing in mind that orbits studied in the present paper are determined by three elements, the authors propose the mean values over time of the squares of velocity components to characterize them.