[en] Time-explicit solutions for relative Keplerian dynamics are presented for the general case in which the reference trajectory is elliptic, parabolic or hyperbolic. The non-linear differential equation modeling the motion is solved by means of tensorial and vectorial regularization methods. This regularizing procedure extends the approaches of Levi-Civita and Kustaanheimo-Stiefel in the case of Kepler problem in rotating reference frames. The solution generalizes the approximate results obtained from Hill-Clohessy-Wiltshire, Lawden and Tschauner-Hempel equations. The approximate solutions derived from the liniarized models are in fact the first linear approximation of the exact solution the authors have found.
Disciplines :
Space science, astronomy & astrophysics
Author, co-author :
Condurache, Daniel; Technical University "Gheorghe Asachi" Iasi, Romania > Theoretical Mechanics
Martinusi, Vladimir ; Technical University "Gheorghe Asachi" Iasi, Romania > Theoretical Mechanics
Language :
English
Title :
A Closed Form Vectorial Solution to the Relative Orbital Motion
Publication date :
01 May 2007
Journal title :
Publications of the Astronomy Department of the Eötvös University
ISSN :
0238-2423
Publisher :
Eötvös University. Astronomy Department, Eötvös, Hungary