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Relative Equilibria in the 3-Dimensional Curved N-Body Problem

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Relative Equilibria in the 3-Dimensional Curved N-Body Problem Synopsis

The author considers the 3 -dimensional gravitational n -body problem, n³2 , in spaces of constant Gaussian curvature K¹0 , i.e. on spheres S 3 ?¹ , for ?>0 , and on hyperbolic manifolds H 3 ?¹, for ?<0 . His goal is to define and study relative equilibria, which are orbits whose mutual distances remain constant in time. He also briefly discusses the issue of singularities in order to avoid impossible configurations. He derives the equations of motion and defines six classes of relative equilibria, which follow naturally from the geometric properties of S 3 ? and H 3 ? . Then he proves several criteria, each expressing the conditions for the existence of a certain class of relative equilibria, some of which have a simple rotation, whereas others perform a double rotation, and he describes their qualitative behaviour.

About This Edition

ISBN: 9780821891360
Publication date:
Author: Florin Diacu
Publisher: American Mathematical Society
Format: Paperback
Pagination: 80 pages
Series: Memoirs of the American Mathematical Society
Genres: Differential calculus and equations
Mathematical physics