Why a rattleback spins one way and reverses the other

Settled in 1986 by G.T. Walker (1896); rigorous general treatment by Hermann Bondi (1986).

The rattleback, or celt, is an asymmetric canoe-shaped top known as an artifact for a long time, but its one-way spin was first given serious scientific attention by G.T. Walker in an 1896 paper. Walker worked out approximate equations showing the effect stems from a slight misalignment between the object's principal moments-of-inertia axes and the symmetry axis of its curved bottom surface, which makes small perturbations grow for one spin sense and damp for the other. A fully general, rigorous rigid-body treatment was given nearly a century later by Hermann Bondi in 1986, putting Walker's approximate analysis on firm mathematical footing.

A lopsided wooden boat-shaped toy spins happily one way but stubbornly refuses the other direction, converting a tiny geometric asymmetry into a dramatic and completely deterministic rebellion against your hand.

Explanations that circulated

• Early explanations attributed the one-way spin simply to the boat-like asymmetric shape without identifying the specific cause: misalignment between the body's principal inertia axes and the geometric axes of its curved bottom.
• The reversal is sometimes wrongly described as violating angular momentum conservation; it is actually a frictional/rolling instability that grows for one spin sense and damps for the other, fully consistent with conservation laws.

References

• The rigid body dynamics of unidirectional spin, Hermann Bondi, Proceedings of the Royal Society of London A, 1986