Abstract
The set of all controls that satisfy the Weierstrass necessary condition for optimality in the problem of time-open, coplanar orbit transfer via impulses is presented, along with the switching relations that must be satisfied at a corner in an optimal trajectory. This includes detailed data for eccentricities near unity. This study takes advantage of recently discovered closed-form solutions for the switching surfaces of this problem.
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Vinh, N. X.,Exact Relations of Optimum Switching in the Problem of Impulsive Transfer, Journal of the Astronautical Sciences, Vol. 17, No. 6, 1970.
Marchal, C.,Transfers Optimaux entre Orbites Kepleriennes. Une Expression des Commutations sous Forme Finie, Astronautica Acta (to appear).
Culp, R. D.,Contensou-Busemann Conditions for Optimal Coplanar Orbit Transfer, AIAA Journal, Vol. 5, No. 2, 1967.
Vinh, N. X., andMarchal, C.,The Lawden's Singular Arcs in a Central Gravitational Field, Paper Presented at the 21st Congress of the International Astronautical Federation, Constance, West Germany, 1970.
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Communicated by T. N. Edelbaum
Portions of this work were supported by NASA Contract No. NASr-54(06) and by NASA Grant No. NGR-06-003-033.
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Vinh, N.X., Culp, R.D. Optimal switching in coplanar orbit transfer. J Optim Theory Appl 7, 197–208 (1971). https://doi.org/10.1007/BF00932478
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DOI: https://doi.org/10.1007/BF00932478