RUS  ENG
Full version
JOURNALS // Regular and Chaotic Dynamics // Archive

Regul. Chaotic Dyn., 2018 Volume 23, Issue 7-8, Pages 961–973 (Mi rcd377)

This article is cited in 1 paper

On the Sectional Curvature Along Central Configurations

Connor Jackmana, Josué Meléndezb

a UC Santa Cruz, 100 High Street Santa Cruz, CA 95064, USA
b UAM–Iztapalapa, San Rafael Atlixco 186, Código Postal 09340, México

Abstract: In this paper we characterize planar central configurations in terms of a sectional curvature value of the Jacobi – Maupertuis metric. This characterization works for the $N$-body problem with general masses and any $1/r^{\alpha}$ potential with $\alpha> 0$. We also obtain dynamical consequences of these curvature values for relative equilibrium solutions. These curvature methods work well for strong forces ($\alpha \geqslant 2$).

Keywords: instability, homographic solutions, central configurations, Jacobi –Maupertuis metric.

MSC: 70F10, 37N05, 70G45

Received: 17.04.2018
Accepted: 06.11.2018

Language: English

DOI: 10.1134/S1560354718070109



Bibliographic databases:


© Steklov Math. Inst. of RAS, 2024