Internal dissipation in the Dzhanibekov effect

Abstract

The Dzhanibekov effect is the phenomenon by which triaxial objects like a spinning wing bolt may continuously flip their rotational axis when initially spinning around the intermediate axis of inertia. This effect is closely related to the Tennis Racket theorem that establishes that the intermediate axis of inertia is unstable. Over time, however, dissipation ensures that a torque free spinning body will eventually rotate around its major axis, in a process called precession relaxation, which counteracts the Dzhanibekov effect. Euler’s equations for a rigid body effectively describe the Dzhanibekov effect, but cannot account for the precession relaxation effect. A dissipative generalization of Euler’s equations displays two dissipative mechanisms: orientational diffusion and viscoelasticity. Here we show through numerical simulations of the dissipative Euler’s equations that orientational diffusion, rather than viscoelasticity, primarily drives precession relaxation and effectively suppresses the Dzhanibekov effect.