Question

Explain the motion of a rattleback. Do not just describe motion Explain the motion.

Answer 1

A toy rattleback is a body having shape of an elongated boat that displays the rattleback effect that
when it is spun about the vertical axis ˆz in the wrong (say clockwise) direction then it slows down,
starts to rattle in longitudinal direction and from this motion acquires the preferred (counterclockwise)
direction of rotation. This behavior is counterintuitive, raises curiosity and seems to be difficult to
explain to a laymen using basic laws of Newtonian mechanics. The rattleback effect is more transparent
when the rattleback is started by tapping a long edge that makes it to oscillate. Then the oscillation
amplitude gradually decreases as the rattleback acquires counterclockwise rotation. Due to presence
of friction and, therefore, dissipation of energy this rotation slows down and after some time stops.
Friction force is always present in any experimental demonstration but it does not seem to be essential
for understanding reversals of the rattleback.
An intuitive understanding of the rattleback effect requires reconciliation of the observed behavior
with our everyday experience about conservation of angular momentum. A change of angular momen-
tum requires a source of torque, which is not directly visible in the rattleback case as it is the reaction
force of the supporting surface that gives rise to the torque.
The purpose of this note is to discuss within vectorial mechanics direction of the reaction force,
the force arm and the torque in the body to see how this torque works in the preferred direction
and reverses sense of rotation. This understanding is based on numerical simulations of a realistic toy rattleback starting with oscillatory initial conditions (IC) or with a slow clockwise rotation. In a
frictionless model rattlebacks energy is conserved and it appears that for low energy initial conditions
also back reversals take place when a rattleback is started with transversal initial oscillations. Long
time solutions appear to be quasiperiodic in agreement with integrable Markeev equations.