Abstract
Necessary and Sufficient Conditionsare known for the problem of the impulsive minimization of thetotal characteristic velocity of a spacecraft subject to linearequations of motions. These conditions are global in the sensethat the primer vector must be known over the entire flight interval.The purpose of the present paper is to present new localizednecessary and sufficiency conditions for the fixed-time problemthat are derived from the original ones, but require informationabout the primer vector only at a few specific points. Thesenew necessary and sufficiency conditions have both theoreticaland practical value.
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References
Hohmann, W., Die Erreichbarkeit der Himmelskörper, Oldenbourg: Munich, Germany, 1925.
Lawden, D. F., Optimal Trajectories for Space Navigation, Butterworths: London, England, 1963.
Lion, P. M., “A primer on the primer,” STAR Memo No. 1, Department of Aerospace and Mechanical Engineering, Princeton University, Princeton, New Jersey, 1967.
Lion, P. M., and Handelsman, M., “Primer vector on fixed-time impulsive trajectories,” AIAA Journal, vol. 6, pp. 127-132, 1968.
Neustadt, L.W., “Optimization, a moment problem, and nonlinear programming,” SIAM Journal on Control, vol. 2, pp. 33-53, 1964.
Neustadt, L. W., “A general theory of minimum-fuel space trajectories,” SIAM Journal on Control, vol. 3, pp. 317-356, 1965.
Edelbaum, T. N., “Minimum-impulse transfers in the near vicinity of a circular orbit,”Journal of the Astronautical Sciences, vol. 14, pp. 66-73, 1967.
Prussing, J. E., “Illustration of the primer vector in the time-fixed orbit transfers,” AIAA Journal, vol. 7, pp. 1167-1168, 1969.
Prussing, J. E., “Optimal two-and three-impulse fixed-time rendezvous in the vicinity of a circular orbit,” AIAA Journal, vol. 8, pp. 1211-1228, 1970.
Prussing, J. E., “Optimal four-impulse fixed-time rendezvous in the vicinity of a circular orbit,” AIAA Journal, vol. 7, pp. 928-935, 1969.
Jones, J. B., “Optimal rendezvous in the neighborhood of a circular orbit,” Journal of the Astronautical Sciences, vol. 24, pp. 53-90, 1976.
Jezewski, D. J., and Donaldson, J. D., “An analytic approach to optimal rendezvous using the Clohessy-Wiltshire equations,” Journal of the Astronautical Sciences, vol. 27, pp. 293-310, 1979.
Jezewski, D., “Primer vector theory applied to the linear relative-motion equations,” Optimal Control Applications and Methods, vol. 1, pp. 387-401, 1980.
Carter, T., “Optimal impulsive space trajectories based on linear equations,” Journal of Optimization Theory and Applications, vol. 70, no. 2, pp. 277-297, 1991.
Carter, T., and Brient, J., “Linearized impulsive rendezvous problem,” Journal of Optimization Theory and Applications, vol. 86, pp. 553-584, 1995.
Carter, T., “Closed-form solution of an idealization of an optimal highly eccentric hyperbolic rendezvous,” Dynamics and Control, vol. 6, pp. 293-307, 1996.
Prussing, J. E., and Clifton, R. S., “Optimal multiple-impulse satellite avoidance maneuvers,” AAS/AIAA Astrodynamics Specialist Conference, Kalispell, Montana, Paper No. AAS-87-543, 1987.
Prussing, J. E., “Optimal impulsive linear systems: sufficient conditions and maximum number of impulses,” Journal of the Astronautical Sciences, vol. 43, no. 2, pp. 195-206, 1995.
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Carter, T.E. Necessary and Sufficient Conditions for Optimal Impulsive Rendezvous with Linear Equations of Motion. Dynamics and Control 10, 219–227 (2000). https://doi.org/10.1023/A:1008376427023
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DOI: https://doi.org/10.1023/A:1008376427023