Dynamics of radial-magnetized microhelix coils

 Radial-magnetized microhelix coils parametrically excited by a magnetic field reveal two distinct types of motion: a rotation at lower excitation frequencies ω_mag ⩽ 250^° s⁻¹ and an oscillatory-like rotative motion at higher frequencies ω^mag ⩾ 300^° s⁻¹, which have been detected experimentally [ E. J. Smith, D. Makarov, S. Sanchez, V. M. Fomin and O. G. Schmidt Phys. Rev. Lett. 107 097204 (2011)]. We provide a theoretical interpretation of this behavior within a model of nonlinear dynamics with parametric excitation by virtue of an interplay between the magnetic and the damping torques acting on the coil. A close fit to the experimental data is achieved if the shape factor of the coil increases from 0.173 for lower frequencies up to 0.276 at higher frequencies. We also predict a transition from the rotation to the oscillatory-like rotative motion that occurs via a regime, where periods of the rotative motion are interrupted by one or more hiccups (back-and-forth motions) of the coil.