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Optimal impulsive space trajectories based on linear equations

  • T. E. Carter
Contributed Papers

Abstract

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 specifieda 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 a spacecraft near a libration point in the restricted three-body problem.

Key Words

Optimization of linear systems optimal space trajectories impulsive maneuvers fuel optimal trajectories minimum characteristic velocity orbital rendezvous linear equations of motion velocity increments 

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Copyright information

© Plenum Publishing Corporation 1991

Authors and Affiliations

  • T. E. Carter
    • 1
  1. 1.Department of Mathematics and Computer ScienceEastern Connecticut State UniversityWillimantic

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