Torques in the (X, Y. Z) and (1, 2, 3) Frames

The torques in the (1, 2, 3) and (X, Y, Z) frames can all be computed from the Euler angle trajectories, so it should be possible to computer simulate the Laithwaite experiment exactly. It is clear that the force due to gravitation is countered by a force due to the gyro, which is a spinning disk on an arm. The arm is horizontal and fixed to a point. Laithwaite holds it at that point. It then appears to be weightless because the internal force it generates is equal and opposite to the force of gravitation on its centre of mass. Before going further however, Eqs. (5) to (7) of Note 368(6) should be checked by computer algebra if this has not already been done.

In a message dated 24/01/2017 20:47:50 GMT Standard Time, writes:

The followin situation is possible, depending on angular momentum constants: In the case m-m1=0 the precession angle phi oscillates around zero, i.e. there is no precession in one direction. However, Laithwait swung the gyro around his body, he could have added an additional torque in this case.

Horst

Am 24.01.2017 um 10:26 schrieb EMyrone:

The nutation and precession of a weightless gyroscope is given by solving Eqs. (10) to (12) simultaneously. So this is the type of motion observed by Laithwaite. A force has been applied in the positive Z axis of the lab frame to counter the force of gravitation.

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