Computation of Periodic Orbits around L1 and L2 using PSO Technique

Abstract

In this work, an optimization problem related to a non-linear function is tackled mathematically by the use of particle swarm optimization (PSO) method in the case of circular restricted three body problem (CRTBP). This method is applied to find the family of periodic orbits around the collinear Lagrangian points $${{L}_{1}}$$ and $${{L}_{2}}$$ in Sun–Earth system. To deal with the chosen like Sun–Earth-spacecraft system, which is constructed as CRTBP problem, the Lagrangian points associated with this system are located by the application of the Newton–Raphson method. Moreover, the initial conditions for periodic orbit of the dynamical system are determined with the same proposed method. The application of the PSO method to this problem is motivated by its higher numerical accuracy.