A closed-form solution to the minimum Lambert’s problem
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A closed form solution to the minimum Vtot2 Lambert problem between two assigned positions in two distinct orbits is presented. Motivation comes from the need of computing optimal orbit transfer matrices to solve re-configuration problems of satellite constellations and the complexity associated in facing these problems with the minimization of Vtot2. Extensive numerical tests show that the difference in fuel consumption between the solutions obtained by minimizing Vtot2 and Vtot2 does not exceed 17%. The Vtot2 solution can be adopted as starting point to find the minimum Vtot2. The solving equation for minimum Vtot2 Lambert problem is a quartic polynomial in term of the angular momentum modulus of the optimal transfer orbit. The root selection is discussed and the singular case, occurring when the initial and final radii are parallel, is analytically solved. A numerical example for the general case (orbit transfer "pork-chop" between two non-coplanar elliptical orbits) and two examples for the singular case (Hohmann and GTO transfers) are provided. © Springer Science+Business Media B.V. 2009.
author list (cited authors)
Avendaño, M., & Mortari, D.