A Graphical Solution of Optimum Time-Fixed Two-Impulse Rendezvous Problem

概要

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A method for numerical determination of optimum time-fixed two-impulse rendezvous between general-inclined noncoapsidal elliptical-orbits is described. In this report, impulse function, that is, required velocity increment, is numerically investigated, and a geometric representation of impulse function in takeoff-arrival time plane is adopted. This geometric representation ("T-space") allows visualization of equi-velocity increment contours, thus revealing the minimum value as a point in this space. At the same time, optimum take-off time and arrival time is also obtained. In addition, by combining these maps, it is possible to obtain an optimum solution to the problem including more than one target, that is, the problem of multi-targets rendezvous. Though this graphical method proves adequate for locating minima of the impulse function, its numerical accuracy is not enough for determination of those precise values. Therefore, McCue's adaptive descent method is employed so that optimum impulse value can be computed accurately.
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