A Closed Form Vectorial Solution to the Relative Orbital Motion

Details A Closed Form Vectorial Solution to the Relative Orbital Motion A Closed Form Vectorial Solution to the Relative Orbital Motion

May 2007

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2007padeu..19...49c&link_type=abstract

Publications of the Astronomy Department of the Eötvös University (PADEU), 2007, ISBN 963 463 557, Vol. 19. Edited by B. Érdi a

Astronomy and Astrophysics

Astronomy

Scientific paper

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.

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