Connor Jackman

University California Santa Cruz


Jackman C., Melèndez J.
On the Sectional Curvature Along Central Configurations
2018, vol. 23, nos. 7-8, pp.  961-973
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
Citation: Jackman C., Melèndez J.,  On the Sectional Curvature Along Central Configurations, Regular and Chaotic Dynamics, 2018, vol. 23, nos. 7-8, pp. 961-973

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