On the dynamics of a spinning top under the influence of rotation: Resonant relative equilibrium states

H. Sheheitli, J. R. Touma

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

We investigate the dynamics of a spinning top driven by a turntable that rotates with a given angular speed Ω. The pivot point of the top is at a fixed distance from the center of the turntable. We show that such a setup leads to resonance where the spinning top is locked in a state of relative equilibrium: precessing with an angular speed equal to that of the turntable while maintaining a constant nutation angle. Bifurcation diagrams are presented to depict how the stability of these relative equilibria, along with the corresponding value of the nutation angle, depends on the two parameters: the initial spin angular momentum and Ω. We discuss the classical spinning top, that is, the Ω=0 case, and address the relation of the “sleeping top” state to the aforementioned relative equilibria. We also relate the dynamics to that of a spherical pendulum on a rotary arm and show that the latter can be viewed as a special case of the system at hand. Finally, we illustrate how the relative equilibria can be exploited for the attitude control of the top through resonance capture while slowly varying the turnable angular speed, Ω.

Original languageEnglish (US)
Pages (from-to)424-436
Number of pages13
JournalCommunications in Nonlinear Science and Numerical Simulation
Volume59
DOIs
StatePublished - Jun 2018
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2017 Elsevier B.V.

Keywords

  • Attitude control
  • Bifurcation
  • Nonlinear resonance
  • Resonance capture
  • Rotation forcing
  • Spinning top

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