All well, the lagrangian of Eq. (1) of Note 6 is the same as the lagrangian in Eq. (10.152) of Marion and Thornton, because the potential energy is U = mgh cos theta. So d cos theta / d theta = – sin theta is used to obtain Eq. (4) of Note 368(6) and eq. (4) of Note 368(7). Your numerical results look good, all kinds of things can be calculated from the trajectories of the Euler angles of the gyroscope.
Sent: 24/01/2017 20:15:48 GMT Standard Time
Subj: Re: 368(7): Nutation and Precession of a Weightless Gyroscope
Shouldn’t there be a minus sign in eq.(4) in front of mgh? It seems that in note 6 this term had the wrong sign in the Lagrangian (1).
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.