Symmetric minimum-impulse rendezvous between certain non-coplanar orbits View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

1970

AUTHORS

Walter Heine , John V. Breakwell

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. More... »

PAGES

130-150

Book

TITLE

Symposium on Optimization

ISBN

978-3-540-04921-0
978-3-540-36275-3

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/bfb0066679

DOI

http://dx.doi.org/10.1007/bfb0066679

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1020824711


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