Journal Article

Relative equilibria in the unrestricted problem of a sphere and symmetric rigid body

Mikhail Vereshchagin, Andrzej J. Maciejewski and Krzysztof Goździewski

in Monthly Notices of the Royal Astronomical Society

Published on behalf of The Royal Astronomical Society

Volume 403, issue 2, pages 848-858
Published in print April 2010 | ISSN: 0035-8711
Published online March 2010 | e-ISSN: 1365-2966 | DOI:
Relative equilibria in the unrestricted problem of a sphere and symmetric rigid body

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We consider the unrestricted problem of two mutually attracting rigid bodies, a uniform sphere (or a point mass) and an axially symmetric body. We present a global, geometric approach for finding all relative equilibria (stationary solutions) in this model, which was already studied by Kinoshita. We extend and generalize his results, showing that the equilibria solutions may be found by solving at most two non-linear, algebraic equations, assuming that the potential function of the symmetric rigid body is known explicitly. We demonstrate that there are three classes of the relative equilibria, which we call cylindrical, inclined coplanar and conic precessions, respectively. Moreover, we also show that in the case of conic precession, although the relative orbit is circular, the point mass and the mass centre of the body move in different parallel planes. This solution has not been known yet in the literature.

Keywords: Celestial mechanics

Journal Article.  6405 words.  Illustrated.

Subjects: Astronomy and Astrophysics

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