Solution of Lambert's Problem for Higher-order Satellite Relative Motion
Abstract
In classical orbital mechanics, the Lambert problem consists of computing the full state of an orbiting body given two positions and the time elapsed between them. Similar analytic methods exist for the relative motion problem, but rely on linearized equations of motion and matrix inversion. In this work, an analytic solution to the "relative" Lambert problem is derived using second-order Clohessy-Wiltshire equations and is applied directly in the relative frame. The problem is represented geometrically by the intersection of three quadric surfaces. The associated multivariate algebraic set is solved non-iteratively using Macaulay resultant expressions to high accuracy.
Recommended Citation
K. A. Le Grand and K. J. De Mars, "Solution of Lambert's Problem for Higher-order Satellite Relative Motion," Advances in the Astronautical Sciences, vol. 152, pp. 2389 - 2403, Univelt, Inc., Jan 2014.
Department(s)
Mechanical and Aerospace Engineering
International Standard Book Number (ISBN)
978-087703611-1
International Standard Serial Number (ISSN)
0065-3438
Document Type
Article - Conference proceedings
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2024 Univelt, Inc., All rights reserved.
Publication Date
01 Jan 2014
