“Hidden ” Momentum in a Linked Pair of Gyrostats

A gyrostat is a massive sphere (or disk) mounted such that the supporting apparatus exerts no torque about the center of the sphere. The earliest gyrostat was described by Bohnenberger [1] in 1817, as shown below. The name gyroscope was applied to this apparatus by Foucault [2] in 1852, although this term has come to imply a sphere or disk mounted with a fixed point on its axis. Lord Kelvin used the term gyrostat in 1874 [3], but in the more modern sense of gyroscope. Consider here a pair of gyrostats joined by a link, as sketched below. Discuss the motion of the system when subject to no external forces, and when the spin angular momentum of the gyrostats is large compared to the orbital angular momentum of the system. This problem is a mechanical analog [4] of a pair of high-spin neutron stars. 1