Satellite oscillations in elliptical orbit

The planar oscillations of a satellite in an elliptical orbit are described by a system of first order canonical differential equations written in terms of a Hamiltonian function which is analytical in a specified range of eccentricities. With sufficiently small values of the eccentricity this system of equations possesses a single parameter family of hyperbolic solutions which attain equilibrium when the eccentricity is zero. The solution of the equation is found for the case of a coordinate system tied to the satellite center of mass and the effect of the eccentricity on satellite oscillation stability is described mathematically. The conditions for a unique periodic solution of the system are also defined. The purely theoretical analysis adduces neither sample calculations nor applications.