Analysis of a Second-Order Relative Motion Lambert Solver


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. Similarly, a relative Lambert problem may cast to determine the relative velocity given two relative positions and the time elapsed between them. When considering linear relative dynamics, the relative Lambert problem may be solved analytically using 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. The method is compared to the linear relative Lambert method as well as the classic Lambert routine.

Meeting Name

AIAA/AAS Astrodynamics Specialist Conference (2014: Aug. 4-7, San Diego, CA)


Mechanical and Aerospace Engineering

Keywords and Phrases

Astrophysics; Orbits; Analytic solution; Clohessy-Wiltshire equations; Macaulay resultant; Matrix inversions; Orbital mechanics; Relative dynamics; Relative positions; Relative velocity; Iterative methods

International Standard Book Number (ISBN)


Document Type

Article - Conference proceedings

Document Version


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© 2014 American Institute of Aeronautics and Astronautics (AIAA), All rights reserved.

Publication Date

01 Aug 2014

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