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Three-Point Charges on a Flexible Arc

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Abstract

We consider equilibrium configurations of three mutually repelling point charges with the Coulomb interaction confined to a simple arc of a constant length with fixed positions of ends. For given values of charges, length of the arc, and distance between its ends, we compute all possible equilibrium configurations. We also study the behavior of equilibrium configurations for variable values of charges and show that the only possible bifurcation is a pitchfork bifurcation. Similar results are presented for elastic loop obeying Hook’s law and for charges interacting via a Riesz potential.

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Authors and Affiliations

  1. Iv. Javakhishvili Tbilisi State University, Tbilisi, Georgia

    G. Giorgadze

  2. Ilia State University, Tbilisi, Georgia

    G. Khimshiashvili

Authors
  1. G. Giorgadze
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  2. G. Khimshiashvili
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Correspondence to G. Giorgadze.

Additional information

Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 177, Algebra, 2020.

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Giorgadze, G., Khimshiashvili, G. Three-Point Charges on a Flexible Arc. J Math Sci 275, 712–717 (2023). https://doi.org/10.1007/s10958-023-06711-8

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  • DOI: https://doi.org/10.1007/s10958-023-06711-8

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