Sitnikov problem in the cyclic kite configuration

This manuscript deals with the development of the series solutions of the Sitnikov kite configuration by the methods given of Lindstedt-Poincarė, using Green’s function and MacMillan. Next we have developed averaged equation of motion by applying the Van der Pol transformation and averaging technique of Guckenheimer and Holmes (Nonlinear oscillations, dynamical system bifurcations of vector fields. Springer, Berlin, 1983). In addition to the resonance criterion at the 3/2 commensurability we have chosen ω=2n/3, n=2, ω is the angular velocity of the coordinate system. Lastly the periodicity of the solutions has been examined by the Poincarė section.