Sitnikov problem: It's extension to four body problem

An analytical expression for the position of the infinitesimal body in the elliptic sitnikov restricted four body problem is presented. this solution is valid for small bounded oscillations in case of moderate eccentricity of primaries. we have linearized the equation of motion to obtain the hill's type equation. using the courant and snyder transformation,hill's equation is transformed into harmonic oscillator type equation. we have used the lindstedt - poincare perturbation method and again we have applied the courant and snyder transformation to obtain the final result. © pakistan academy of sciences.