Solutions of the Sitnikov Restricted Four Body Problem: an Analytic Approximate Solution of the Sitnikov Four Body Problem

Solutions of the Sitnikov restricted four body problem have been found when all the primaries are sources of radiation. We have found the averaged Hamiltonian of the system and its solution in term of Elliptic integrals. Using Lindstedt-Poincare method, we have obtained the solutions of Hill's equation. By using Courant and Snyder transformation we have solved the Harmonic oscillator type equation, transformed by Hill?s Equation. As we are dealing with the elliptic case of the Sitnikov four body problem, the Equation [2.53] is unperturbed system. There is the perturbation in the z-direction as well. It is observed that the effect of nonlinear term is to shift the frequency as a function of the amplitude and to distort the trajectory z(t), introducing harmonics of the shifted linear oscillator frequency. In Chapter-4, the problem is being investigated by two different methods: (1) Solutions by Lindstedt-Poincare method, (2) Solutions by using Green?s function. This book is extremely useful to post graduate students, research scholars, scientists who are interested in restricted three body problem and Sitnikov problem.