  We report the counter-intuitive instability of charged elastic rings, and the
persistence of sinusoidal deformations in the lowest-energy configurations by
the combination of high-precision numerical simulations and analytical
perturbation calculation. We also study the dynamical evolution of the charged
ring under random disturbance, and reveal the modulation of the dominant
frequencies by the electrostatic force. The purely mechanical analysis of the
classical ring system presented in this work yields insights into the subtlety
of long-range forces in the organization and dynamics of matter.
