Relative equilibria in the 3-dimensional curved n-body problem
著者
書誌事項
Relative equilibria in the 3-dimensional curved n-body problem
（Memoirs of the American Mathematical Society, no. 1071）
American Mathematical Society, c2013
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Relative equilibria in the three-dimensional curved n-body problem
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注記
"March 2014, volume 228, number 1071 (third of 5 numbers)."
Includes bibliographical references (p. 77-80)
内容説明・目次
内容説明
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.
目次
Introduction
Background and equations of motion
Isometries and relative equilibria
Criteria and qualitative behaviour
Examples
Conclusions
Bibliography
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