We find periodic solutions of the Coulomb d-dimensional (d = 1, 2, 3) equations of motion for two identical negative point charges in the field of four identical positive point charges fixed at vertices of a rectangle. Systems of this kind have equilibrium configurations. Periodic solutions are obtained with the help of the Lyapunov center theorem.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 72, No. 10, pp. 1432–1442, October, 2020. Ukrainian DOI: 10.37863/umzh.v72i10.741.
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Skrypnik, W.I. Periodic Coulomb Dynamics of Two Identical Negative Charges in the Field of Four Identical Fixed Positive Charges. Ukr Math J 72, 1650–1663 (2021). https://doi.org/10.1007/s11253-021-01878-2
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DOI: https://doi.org/10.1007/s11253-021-01878-2