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Optimal impulsive space trajectories based on linear equations. (English) Zbl 0732.49025
The problem of minimizing the total characteristic velocity of a spacecraft having linear equations of motion and finitely many instantaneous impulses that result in jump discontinuities in velocity is considered. Fixed time and fixed end conditions are assumed. This formulation is flexible enough to allow some of the impulses to be specified a priori by the mission planner. Necessary and sufficient conditions for solution of this problem are found without using specialized results from control theory or optimization theory. Solution of the two point boundary value problem is reduced to a problem of solving a specific set of equations. If the times of the impulses are specified, these equations are at most quadratic. Although this work is restricted to linear equations, there are situations where it has potential application. Some examples are the computation of the velocity increments of a spacecraft near a real or fictitious satellite or space station in a circular or more general Keplerian orbit. Another example is the computation of maneuvers of the spacecraft near a libration point of the restricted three-body problem.
Reviewer: T.E.Carter
MSC:
49N70Differential games in calculus of variations
49N75Pursuit and evasion games in calculus of variations
93C05Linear control systems
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