Optimal Trajectory Design of an Upper Stage for Satellite Injection into Geostationary Orbit Using Limited Thrust

In this research, the problem of optimal trajectory design of an upper stage is considered for satellite injection into Geostationary orbit in 3-Dimensional space. The optimal multi-burn trajectory is obtained based on Euler-Lagrange theory with minimum fuel consumption criteria. Instead of using switch function for obtaining the switching times, which complicates the numerical solution of the optimal control problem, the presented algorithm uses a simple and optimal process to find the burn and coast times. To solve the tow point boundary value problem, an improved indirect shooting method with high performance is used which in addition to having higher precision, converges very fast to the desired condition.