Lord Kelvin's gyrostat and its analogs in physics, including the Lorenz model

A gyrostat is a system of bodies whose relative motion does not alter the intrinsic mass distribution of the system. A solid gyrostat is an arbitrary rigid body attached to one or more axisymmetric rotors with their axes fixed in the carrier. A liquid gyrostat is a cavity in a rotating rigid body filled with an inviscid, homogeneous fluid. For certain conditions, gyrostats obey the Volterra equations of motion, a generalization of the Euler equations for a rigid body rotating about a fixed point. The Lorenz model is equivalent to a special case of a gyrostat in a forced, dissipative regime, as is its laboratory analog, the Malkus water wheel. Over a century ago, Lord Kelvin, the gyrostat's inventor, attempted to formulate mechanical models of the elasticity of matter and the ether, using lattices of linked gyrostats. Opportunities for using gyrostats in the teaching of undergraduate mechanics, nonlinear dynamics, and fluid dynamics are discussed.