Nonlinear Stability Analysis of Elliptical restricted three body problem

The elliptical restricted three body problem describes the motion of a particle called third body (infinitesimal mass) under the gravitational attraction forces of two finite bodies called the primaries which revolve on the elliptic orbits in a plane around their common center of mass. In the restricted problems the motion of two finite bodies (called primaries) satisfies the differential equation governing the dynamics of two body problem. Hence the primaries may describe in circular elliptical parabolic or hyperbolic orbits. In the case when the primaries move along a circular orbit then it is called circular restricted three body problem and if the primaries move on the elliptic orbit then it is called Elliptical restricted three body problems. The restricted problem of these bodies (circular or elliptical) is widely application in space Dynamics Celestial Mechanics Cosmology and Stellar dynamics.