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1984•The Astrophysical JournalRequires access

Stellar orbits in angle variables

S. J. Ratcliff, K. M. Chang, M. Schwarzschild

Open publisher page 21 citations

Abstract

Following recent basic developments by Binney and Spergel, the equations of motion for a star in a galactic potential have been transformed from time to angle variables. A numerical procedure has been devised to solve the transformed equations for two-dimensional box and loop orbits in the equatorial plane of a triaxial potential. In this procedure an orbit is specified not by its starting values in phase space, but either by its frequencies or by its action values. A substantial set of orbits has been derived by this procedure for one potential. The results for their physical and geometrical characteristics are displayed in action diagrams.

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What this paper is about

Following recent basic developments by Binney and Spergel, the equations of motion for a star in a galactic potential have been transformed from time to angle variables. A numerical procedure has been devised to solve the transformed equations for two-dimensional box and loop orbits in the equatorial plane of a triaxial potential. In this procedure an orbit is specified not by its starting values in phase space, but either by its frequencies or by its action values. A substantial set of orbits has been derived by this procedure for one potential. The results for their physical and geometrical characteristics are displayed in action diagrams.

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Available abstract

Following recent basic developments by Binney and Spergel, the equations of motion for a star in a galactic potential have been transformed from time to angle variables. A numerical procedure has been devised to solve the transformed equations for two-dimensional box and loop orbits in the equatorial plane of a triaxial potential. In this procedure an orbit is specified not by its starting values in phase space, but either by its frequencies or by its action values. A substantial set of orbits has been derived by this procedure for one potential. The results for their physical and geometrical characteristics are displayed in action diagrams.

Key concepts: Physics, Celestial mechanics, Orbit (dynamics), Phase space, Schwarzschild radius, Equations of motion, Action (physics), Astrometry

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