Saari's conjecture for the collinear n-body problem

被引：35

作者：

Diacu, F

Perez-Chavela, E

Santoprete, M

机构：

[1] Univ Victoria, Pacific Inst Math Sci, Victoria, BC V8W 3P4, Canada

[2] Univ Victoria, Dept Math & Stat, Victoria, BC V8W 3P4, Canada

[3] Univ Autonoma Metropolitana Iztapalapa, Dept Matemat, Mexico City 09340, DF, Mexico

[4] Univ Calif Irvine, Dept Math, Irvine, CA 92697 USA

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2005年 / 357卷 / 10期

关键词：

D O I：

10.1090/S0002-9947-04-03606-2

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In 1970 Don Saari conjectured that the only solutions of the Newtonian n-body problem that have constant moment of inertia are the relative equilibria. We prove this conjecture in the collinear case for any potential that involves only the mutual distances. Furthermore, in the case of homogeneous potentials, we show that the only collinear and non-zero angular momentum solutions are homographic motions with central configurations.

引用

页码：4215 / 4223

页数：9