Forced precession in a spinning wheel supported on a rotating pivot

• We analyzed a spinning wheel of which the pivot is not fixed but forced to rotate.
• We introduced a fourth Euler angle related to the motor (forced precession).
• We investigated two types of joints between rotating arm and wheel's axle.
• We clarified the energy exchange between the experimentist (motor) and the gyro.
• We explained the biomechanics involved in Laithwaite's classical gyro experiment.

This paper deals with the mechanics involved in a spinning wheel of which the pivot is not fixed as usual but is forced to rotate along the circumference of a circle on the horizontal plane. The usual Euler equations are extended so that, in addition to the three well-known rotations (Euler angles), they also include a fourth one related to the rotation of the motor that induces the forced precession. This study aims at offering a first insight in one of the renowned Laithwaite's experiments. The derived theoretical expressions are accompanied by computer simulation.