Trajectory Optimization for a Single Stage Launcher with Constrained Conditions

Trajectory optimization aims to position launcher vehicles into a desired orbit in a minimum flight time with a maximum mass. Algorithms based on the Optimal Control Theory are successfully implemented to optimize trajectories for a long time. Initially, depends on the optimization requirements, cost function of the Optimal Control is put forward. Next, state and costate equations are formed. Then, initial, and final boundary conditions are combined with the differential equations. Efficient and accurate methods are required to solve these complicated and sometimes non-linear coupled ordinary differential equations. In this study, we implement a second order correct, time reversible Leapfrog method to solve these equations and optimize trajectory. Then we compare the results with MATLAB's TPBVP solver called bvp5c. Even if these two solvers are used different time to orbit and steering angle values, both methods place the launch vehicle to same orbit with same velocity components.