Many thanks, this must be the motion observed by Laithwaite. There are finite moments of inertia because there is still an m. It is effectively cancelled by an applied m1. The latter originates in a potential due to a lifting force. So the complete potential energy is (m – m1) g h cos theta which vanishes when m = m1. The moments of inertia are still defined by m as usual.
Sent: 24/01/2017 09:41:47 GMT Standard Time
Subj: Re: 368(7): Nutation and Precession of a Weightless Gyroscope
I computed the solutions for the weighless gyroscope (m=0), see third and fourth graph of the attachment. The results remain similar but angle variations are smaller. I am not sure how to interpret this. We have moments of inertia as before but no mass. The parameters have to be studied additionally. For example I_12 = I_3 seems to be a special case where some terms in the Lagrangian vanish.
I am out of house for the rest of the day.
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.