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This article is cited in 1 scientific paper (total 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.
Received: 17.04.2018 Accepted: 06.11.2018
Citation:
Connor Jackman, Josué Meléndez, “On the Sectional Curvature Along Central Configurations”, Regul. Chaotic Dyn., 23:7-8 (2018), 961–973
Linking options:
https://www.mathnet.ru/eng/rcd377 https://www.mathnet.ru/eng/rcd/v23/i7/p961
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Abstract page: | 154 | References: | 21 |
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