Abstract
An approximate method is given for determining the optimal trajectory of a thrust-limited rocket transferring from one known elliptic orbit to another in a vacuum. The trajectory consists of thrust-coast-thrust arcs, and the deviation from the initial orbital plane is of first-order smallness compared to the path projected onto the plane.
In its application, no more than two degrees are iterated concurrently, the first pair to meet the in-plane requirements and the second to satisfy the out-of-plane conditions. It is also shown that since second-order terms were neglected, the approximation in fuel expenditure is of fourth order.
We include an example in order to demonstrate the feasibility of the method.
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References
Fraeijs de Veubeke, B., "Canonical Transformations and the Thrust-Coast-Thrust Optimal Transfer Problem," Astronautica Acta, Vol. 11, No. 4, 1965, pp. 271–282.
Fraeijs de Veubeke, B., "Optimal Steering and Cutoff — Relight Programs for Optimal Transfers," Astronautica Acta, Vol 12, No. 4, 1966, pp. 323–328.
Lawden, G. H., "Trajectory Optimization for a Rocket with a Generalized Thrust Characteristic," Astronautica Acta, Vol X, Fasc. 5–6, 1964, pp 279–295.
Moskowitz, S., "On the Accuracy of Approximate Thrust Steering Schedules in Optimal Correctional Maneuvers," Astronautica Acta, Vol 9, No. 1, 1963, pp 20–30.
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Ting L., "Approximations in Variational Problems," Aero/Space Engng, Vol 20, 1961, pp 32–33, 89–91.
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© 1970 Springer-Verlag
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Moskowitz, S.E. (1970). Approximate non-coplanar orbital transfers with minimum expenditure of fuel. In: Balakrishnan, A.V., Contensou, M., de Veubeke, B.F., Krée, P., Lions, J.L., Moiseev, N.N. (eds) Symposium on Optimization. Lecture Notes in Mathematics, vol 132. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0066687
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DOI: https://doi.org/10.1007/BFb0066687
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