On the geometry and behavior of n-body motions

The kinematic separation of size, shape, and orientation of n-body systems is investigated together with specific issues concerning the dynamics of classical n-body motions. A central topic is the asymptotic behavior of general collisions, extending the early work of Siegel, Wintner, and more recent...

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Main Author: Eldar Straume
Format: Article
Language:English
Published: Wiley 2001-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Online Access:http://dx.doi.org/10.1155/S016117120100669X
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author Eldar Straume
author_facet Eldar Straume
author_sort Eldar Straume
collection DOAJ
description The kinematic separation of size, shape, and orientation of n-body systems is investigated together with specific issues concerning the dynamics of classical n-body motions. A central topic is the asymptotic behavior of general collisions, extending the early work of Siegel, Wintner, and more recently Saari. In particular, asymptotic formulas for the derivatives of any order of the basic kinematic quantities are included. The kinematic Riemannian metric on the congruence and shape moduli spaces are introduced via O(3)-equivariant geometry. For n=3, a classical geometrization procedure is explicitly carried out for planary 3-body motions, reducing them to solutions of a rather simple system of geodesic equations in the 3-dimensional congruence space. The paper is largely expository and various known results on classical n-body motions are surveyed in our more geometrical setting.
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spelling doaj-art-b2abd90bdf1a4fd791ec54ff948407782025-08-20T02:23:18ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252001-01-01281268973210.1155/S016117120100669XOn the geometry and behavior of n-body motionsEldar Straume0Department of Mathematical Sciences, Norwegian University of Science and Technology, Trondheim N-7491, NorwayThe kinematic separation of size, shape, and orientation of n-body systems is investigated together with specific issues concerning the dynamics of classical n-body motions. A central topic is the asymptotic behavior of general collisions, extending the early work of Siegel, Wintner, and more recently Saari. In particular, asymptotic formulas for the derivatives of any order of the basic kinematic quantities are included. The kinematic Riemannian metric on the congruence and shape moduli spaces are introduced via O(3)-equivariant geometry. For n=3, a classical geometrization procedure is explicitly carried out for planary 3-body motions, reducing them to solutions of a rather simple system of geodesic equations in the 3-dimensional congruence space. The paper is largely expository and various known results on classical n-body motions are surveyed in our more geometrical setting.http://dx.doi.org/10.1155/S016117120100669X
spellingShingle Eldar Straume
On the geometry and behavior of n-body motions
International Journal of Mathematics and Mathematical Sciences
title On the geometry and behavior of n-body motions
title_full On the geometry and behavior of n-body motions
title_fullStr On the geometry and behavior of n-body motions
title_full_unstemmed On the geometry and behavior of n-body motions
title_short On the geometry and behavior of n-body motions
title_sort on the geometry and behavior of n body motions
url http://dx.doi.org/10.1155/S016117120100669X
work_keys_str_mv AT eldarstraume onthegeometryandbehaviorofnbodymotions