On the Sectional Curvature Along Central Configurations

    2018, Volume 23, Numbers 7-8, pp.  961-973

    Author(s): Jackman C., Melèndez J.

    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, Volume 23, Numbers 7-8, pp. 961-973

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