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  • A method for determining optimal fixed-time, N-impulse trajectories between arbitrarily inclined orbits

    Paper ID



    • Donald J. Jezewski


    NASA Manned Spacecraft Center






    A method has been developed that uses primer- vector theory to determine the time, number, and state vector of all impulses and the true anomalies in the initial and final orbits. This method optimizes fixed-time, N-impulse trajectories between arbitrarily inclined orbits. The N-impulse solutions obtained are optimal in that the velocity cost function exhibits at least a local minimum. The necessary conditions for local optimality are assured (l) by requiring continuity of the primer vector, the primer-vector derivative, and the Hamiltonian at all interior junction points and (2) by requiring that the Hamiltonian be zero for the optimal departure and arrival true anomalies. An example problem for which three impulses were determined to be optimal is presented for a range of transfer times, inclinations, and ascending nodes of the final orbit. Results indicate that the free condition on the true anomalies produced bielliptic-type transfers for the solutions investigated.