The optimal conditions for spatial impulsive maneuvers with time constraint approached from functional optimization are established. Equations of Lawden's constants computed from boundary parameters of a coasting arc are given. The determination of the optimal number of impulses and the criteria for moving an impulse from the terminal point to an interior point are established by observing the behavior of the primer vector throughout the transfer period. The time of flight equation is modified for the possibility of multiple revolutions. Some experiences on using the homotopy method to solving n independent variables from n nonlinear algebraic equations are discussed. Choosing the suitable independent variables for some limiting cases to find the critical value is introduced. The linearized solution for a time-free transfer between two nearly aligned coplanar ellipses is obtained from perturbation theory.
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