On Orbits for a Particular Case of Axial Symmetry

A particular case of steady state and axial symmetry - the potentialformula proposed by Miyamoto and Nagai - is studied. A number of orbits of abound test particle is determined numerically, with both, the potentialparameters and initial conditions, varied. Unlike special cases, such asnearly circular and nearly planar orbits, in the case of "truly spatial orbits" the time dependence of the coordinates becomes very complicated and amathematical treatment including any known periodic functions is hardlypossible. Bearing in mind that orbits studied in the present paper aredetermined by three elements, the authors propose the mean values over time ofthe squares of velocity components to characterize them