Analytical Solutions of the Relative Motion About a Keplerian Elliptic Orbit
- Paper number
IAC-11,C1,3,2,x9672
- Author
Prof. Gerard Gomez, University of Barcelona, Spain
- Coauthor
Mr. Manuel Marcote, Deimos Space S.L., Spain
- Coauthor
Prof. Josep J. Masdemont, Universitat Politecnica de Catalunya (UPC), Spain
- Coauthor
Dr. Yuan Ren, Spain
- Year
2011
- Abstract
The purpose of this paper is to obtain a third-order expression, in the in-plane and out-of-plane amplitudes, of the solutions of the elliptic Hill-Clohessy-Wiltshire non-linear equations. The coefficients of the 3rd-order expansions of the coordinates are given as explicit functions of the eccentricity e of the orbit of the leader. For e = 0 we recover the solution given by Richardson and Mitchell for the circular case; for e different from zero, the linear terms of the solution recover the solution found by Lawden for the linearised elliptic HCW equations, also known as the Tschauner–Hempel equations. In the last part of the paper we explain the how a formal series solution of the elliptic HCW non-linear equations (in powers of the two amplitudes and the eccentricity) can be obtained, using the Lindstedt-Poincaré procedure.
- Abstract document
- Manuscript document
IAC-11,C1,3,2,x9672.pdf (🔒 authorized access only).
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