Optimal trajectories based on linear equations
Abstract
The Principal results of a recent theory of fuel optimal space trajectories for linear differential equations are presented. Both impulsive and boundedthrust problems are treated. A new form of the Lawden Primer vector is found that is identical for both problems. For this reason, starting iteratives from the solution of the impulsive problem are highly effective in the solution of the twopoint boundaryvalue problem associated with bounded thrust. These results were applied to the problem of fuel optimal maneuvers of a spacecraft near a satellite in circular orbit using the ClohessyWiltshire equations. For this case twopoint boundaryvalue problems were solved using a microcomputer, and optimal trajectory shapes displayed. The results of this theory can also be applied if the satellite is in an arbitrary Keplerian orbit through the use of the TschaunerHempel equations. A new form of the solution of these equations has been found that is identical for elliptical, parabolic, and hyperbolic orbits except in the way that a certain integral is evaluated. For elliptical orbits this integral is evaluated through the use of the eccentric anomaly. An analogous evaluation is performed for hyperbolic orbits.
 Publication:

Flight Mechanics/Estimation Theory Symposium, 1990
 Pub Date:
 December 1990
 Bibcode:
 1990fmet.symp..539C
 Keywords:

 Boundary Value Problems;
 Circular Orbits;
 Differential Equations;
 Elliptical Orbits;
 Linear Equations;
 Spacecraft Maneuvers;
 Spacecraft Trajectories;
 Thrust;
 Anomalies;
 Microcomputers;
 Optimization;
 Shapes;
 Astrodynamics