Coordinate system influence on the numerical solution of the trajectory optimization problem



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A theoretical development and comparative evaluation is made by formulating the trajectory optimization problem in several different coordinate systems. Particular attention is given to the sensitivity of the convergence characteristics, convergence times, and computer logic. This study is initiated by formulating the two-body problem of orbital mechanics in six different coordinate systems. Having the closed-form solution of this problem allows the comparison of the numerical error generation in the different coordinate systems. Based upon the results of the two-body study, three coordinate systems are chosen for the optimization study. The problem is to determine the control program which will move a spacecraft from a circular Earth orbit to escape velocity under continuous low thrust in minimum time. A perturbation method is used to solve the nonlinear two-point boundary value problem associated with the optimization problem. A modified correction technique is proposed and preliminary results are presented.