On the geometry and behavior of \(n\)-body motions
type: Item
instance of: scholarly article
title: On the geometry and behavior of \(n\)-body motions
zbMATH Open document ID: 1014.70013
DOI: 10.1155/S016117120100669X
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2002-08-13T00:00:00Z
full work available at URL: https://eudml.org/doc/50105
full work available at URL: S016117120100669X.html
review text: Summary: 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, we give asymptotic formulas for the derivatives of any order of basic kinematic quantities. 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 carried out explicitly for planar three-body motions, reducing them to solutions of a rather simple system of geodesic equations in three-dimensional congruence space. The paper is largely expository, and various known results on classical \(n\)-body motions are surveyed in our more geometrical setting.
Mathematics Subject Classification ID: 70F10
Mathematics Subject Classification ID: 70G45
Mathematics Subject Classification ID: 70F16
zbMATH DE Number: 1780308
zbMATH Keywords: asymptotic behavior of collisions
zbMATH Keywords: kinematic Riemannian metric
zbMATH Keywords: shape moduli spaces
zbMATH Keywords: \(O(3)\)-equivariant geometry
zbMATH Keywords: geometrization procedure
zbMATH Keywords: geodesic equations
zbMATH Keywords: three-dimensional congruence space
zbMATH Keywords: \(n\)-body motions
author: Eldar Straume
MaRDI profile type: Publication
Wikidata QID: Q125575983
OpenAlex ID: W1997192990
description: scientific article; zbMATH DE number 1780308