The motion of a globular cluster inside a rotating,layered, inhomogeneous elliptical galaxy

We consider the spatial motion of a globular cluster with a constant or variable mass inside a rotating, layered, inhomogenous elliptical galaxy with a constant or variable mass. An analog to the Jacobi integral is found, regions of possiblemotion are determined, and zero-velocity surfaces constructed. Stationary solutions (libration points) are determined, together with their stability according to the Lyapunov criterion. In the case of variable mass, the autonomization method is used to solve the equations of motion, and the autonomization criteria used to establish an analog of the Eddington-Jeans law for the variation of the density of the galaxy.