Description of the Orbital Motions

Abstract

At the heart of any description of a stellar system lies some representation of the way the stars in the system move around. We will start by looking at the motion of individual stars within the galaxies, show how their motions are determined, and introduce different notations that will prove useful in the description of these motions. We will consider three kinds of systems in this book, spherical systems, axisymmetric systems and disc systems. The last is really a subclass of the first set. Although elliptical galaxies are probably triaxial, in this chapter we are establishing the dynamics of unstable initial states rather than modelling the final state of the system. We restrict ourselves, therefore, without much loss of generality to models with at least one axis of symmetry. The results derived in this chapter will provide the groundwork for the next chapter where we shall consider the effects of perturbing the equilibrium potential that governs the motions of the stars.