OK many thanks, the method allows for any lab frame torque, not only the gravitational torque, so the kind of torque used by Laithwaite can be simulated. The net effect of his torque was to lift the gyro to the height of his outstretched arm, so its net effect can be simulated with a simple force in the plus Z direction in addition to the force generated by the gyro itself. Also a force due to the convective derivative can also be added. So I will now write up Sections 1 and 2. The Euler angle analysis of the gyro is exceedingly complicated, there may never have been a complete Euler angle solution prior to this work. The coding of molecular dynamics computer simulation algorithms such as TETRA (complete FORTRAN code on www.aias.us) may have used an equivalent method using a different way to relate frame (1, 2, 3) to frame (X, Y, Z). I computed cross correlations between rotation and translation in both frames (Omnia Opera circa 1976 to circa 1993). The Evans / Pelkie animation on youtube shows that the code worked perfectly and shows what is in effect the motion of 108 gyro’s interacting with pairwise additive Lennard-Jones atom atom potentials.
Sent: 25/01/2017 14:50:27 GMT Standard Time
Subj: Re: Writing Up UFT368
The numerical solution of the Lagrange equations seems to be valid. I will still check the latest notes in more detail and describe the solution with some graphics in section 3. We will have to discern cases with
L_psi>L_phi, L_psi<L_phi etc.
as is described in M&T.
Am 25.01.2017 um 14:33 schrieb EMyrone:
I will proceed to writing up UFT368 Sections 1 and 2 – the first complete solution of the gyroscope problem. The motion is exceedingly rich and intricate, and in general the general solution allows any kind of additional lab frame torque to be considered. In addition to these dynamics, a vacuum induced torque can also be considered by considering the convective derivative of angular momentum.