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Optimal Low-Thrust Spacecraft Trajectories Using Time-Domain Finite Element Method

In this study, optimal low-thrust spacecraft trajectories are obtained by time-domain finite element method. Equations of motion are expressed in state-space form. The performance index is considered as minimum time. The problem has been formulated through the variational approach. The time-domain finite element discretized form of the performance index, state equation constraints and the related boundary conditions are presented. By setting out the discrete equations, a set of nonlinear algebraic equations is generated and by using Newton-Raphson method, optimum answer is attained. The effects of the number of time segments on the performance index are examined. Furthermore, the influences of effective exhaust velocities on the optimal trajectory are demonstrated