Adaptive two-point boundary value problem tool for accurate and efficient computation of perturbed orbit transfers

We have developed a parallel compiled code tool that combines several of our recently developed methods for solving the perturbed Lambert problem using Modified Chebyshev Picard Iteration (MCPI). This tool consists of four individual algorithms, each of which is unique and better suited for solving a particular type of orbit transfer than the others. The first uses the standard MCPI two-point boundary value problem (TPBVP) solver and converges over about one third of an orbit. The second uses the Method of Particular Solutions (MPS) and Picard iteration for solving multi-revolution two-impulse transfers. The third is similar to the first but is capable of solving optimal control low thrust transfers. This algorithm is also convergent over about one third of an orbit. The fourth is again similar to the second but here we use MPS in six dimensions to solve the optimal control problem over multiple revolutions. In this paper we present four example test cases to demonstrate the accuracy and efficiency of our TPBVP algorithm compared with a Newton-type shooting method where RK12(10) is used as the numerical integrator. In all four cases our algorithm is more efficient while maintaining machine precision accuracy.