Abstract
A three-parameter family of optimal rendezvous maneuvers is investigated, describable as follows: rendezvous is to be accomplished in a specified time-interval between two equi-energy near-circular slightly non-coplanar orbits whose line-of-nodes is traversed exactly at mid-time; the required total displacement of the "vacant" focus during the rendezvous is perpendicular to the line-of-nodes; lastly, the required in-track position change is, like the eccentricities and the plane change, a small quantity. The three essential parameters for this family are the two ratios of the three small quantities Δe⊥, i, and Δ*ϑ, together with the total angular travel (not small) by either vehicle, where Δe⊥ is the change of the eccentricity component perpendicular to the line of nodes, i is the plane rotation, and Δ*ϑ is a suitable in-track phase change.
The optimal rendezvous maneuvers for this family consists of pairs of equal impulses symmetrically spaced about the mid-position (including possibly an impulse at the mid-position), the forward component of the impulse being reversed within each pair.
The optimal number of impulses varies from one to six. For cases in which Δe⊥/i exceeds 1/√3 there is, as in the time-free near-circular problem, a degeneracy, at least if Δ*ϑ/Δe⊥ lies within a certain range, the location of the impulses being no longer unique. In such cases the number of impulses need never exceed six, however.
A one-parameter family of charts is presented, indicating regions requiring different numbers of impulses, in some cases with an initial and final coasting period, and indicating the degenerate region, if any. A separate chart permits the selection of a variety of optimal impulsive maneuvers in the degenerate cases.
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References
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© 1970 Springer-Verlag
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Heine, W., Breakwell, J.V. (1970). Symmetric minimum-impulse rendezvous between certain non-coplanar orbits. 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/BFb0066679
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DOI: https://doi.org/10.1007/BFb0066679
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