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A Study of Time-Optimal Rendezvous in Three Dimensions, Volume I

Report Number: AFFDL TR 65-20 Volume 1
Author: Paiewonsky, B. H.
Author: Woodrow, P. J.
Corporate Author: Aeronautical Research Associates of Princeton, Inc.
Laboratory: Air Force Flight Dynamics Laboratory
Date of Publication: 1965-01
Pages: 77
Contract: AF 33(657)-11319
Project: 8219
Task: 821904
AD Number: AD0624218

The results of a study of time optimal rendezvous in three dimensions with bounds on the rocket thrust and the available propellant are described. The equations of motion are linearized and Neustadt's method is used to solve the two-point boundary value problem in the seven-dimensional state space. Three convergence acceleration schemes are studied. Examples of terminal rendezvous paths are presented and discussed in terms of the magnitudes of the bounds on thrust and fuel. The dependence of terminal errors on initial measurement errors in position and velocity is also discussed. The range of initial values include position errors up to 25 miles and relative velocity errors of 200 ft/sec. The thrust accelerations of the rockets are on the order of 1 ft/sec-sq; the propellant bounds (ideal characteristic velocities) range between 600 ft/sec and 250 ft/sec.

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