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On the Sectional Curvature Along Central Configurations

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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/rα potential with α > 0. We also obtain dynamical consequences of these curvature values for relative equilibrium solutions. These curvature methods work well for strong forces (α ≥ 2).

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Authors and Affiliations

  1. UC Santa Cruz, 100 High Street, Santa Cruz, CA, 95064, USA

    Connor Jackman

  2. UAM–Iztapalapa San Rafael Atlixco 186, Código Postal, 09340, México

    Josué Meléndez

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  1. Connor Jackman
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  2. Josué Meléndez
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Correspondence to Connor Jackman.

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Jackman, C., Meléndez, J. On the Sectional Curvature Along Central Configurations. Regul. Chaot. Dyn. 23, 961–973 (2018). https://doi.org/10.1134/S1560354718070109

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  • DOI: https://doi.org/10.1134/S1560354718070109

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