A closed-form solution to the minimum Delta V-tot(2) Lambert's problem

作者：Avendano Martin; Mortari Daniele^*

来源：Celestial Mechanics and Dynamical Astronomy, 2010, 106(1): 25-37.

DOI：10.1007/s10569-009-9238-x

• Orbit transfer
• Two-impulse
• Rendezvous
• Lambert's problem

A closed form solution to the minimum Delta V-tot(2) 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 Delta V-tot. Extensive numerical tests show that the difference in fuel consumption between the solutions obtained by minimizing Delta V-tot(2) and Delta V-tot does not exceed 17%. The Delta V-tot(2) solution can be adopted as starting point to find the minimum Delta V-tot. The solving equation for minimum Delta V-tot(2) 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.

• 出版日期2010-1