Systems with a preferred spin direction

This paper investigates the dynamics of systems that are inclined to rotate in only one direction. When rotated in the other direction they are unstab le and eventually reverse their direction of rotation. This non-Hamiltonian behaviour is caused by non-holonomic constraints. The most well-known exam ple is the so-called rattleback, but here we mainly investigate a simpler m odel, presumably the simplest possible. As an illustration that non-holonom ic constraints cause unusual dynamics we show that an arbitrary dynamical s ystem is contained in a Lagrangian system with non-holonomic constraints.