Internal dissipation in the tennis racket effect

Abstract

The phenomenon known as the tennis racket effect is observed when a rigid body experiences unstable rotation around its intermediate axis. In free space, this leads to the Dzhanibekov effect, where triaxial objects like a spinning wing bolt may continuously flip their rotational axis. 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 tennis racket effect. Euler's equations for a rigid body effectively describe the tennis racket effect, but cannot account for the precession relaxation effect. A recent theory has put forward a generalization of Euler's equations that includes dissipation in a thermodynamically consistent way. The theory displays two dissipative mechanisms: orientational diffusion and viscoelasticity. Here we show that orientational diffusion, rather than viscoelasticity, primarily drives precession relaxation and effectively suppresses the tennis racket effect.

6 pages, 2 figures