370(2): Gyro Subjected to the General External Torque

Thanks again, the computer indicates that Eq. (10) cannot be used, so Note 370(4) should be used and Note 370(2) not used.

To: EMyrone@aol.com
Sent: 12/02/2017 19:28:17 GMT Standard Time
Subj: Re: 370(2): Gyro Subjected to the General External Torque

I checked the equations. As I argued, introducing a variable r that is not a Lagrange variable and replacing it by other variables in some cases, gives no meaningful results. See sect. 4.4 in the protocol. The only meaningful method is to treat r as an independent variable, then no replacements like (10) cannot be made. I think this note is obsolete and has been replaced by later notes.


Am 09.02.2017 um 12:27 schrieb EMyrone:

This note deals with a force applied directly upwards to the point of the gyro, as described in Fig. (1). Subject to checking by computer algebra the lagrangian analysis gives the four simultaneous equations (20) to (23), in the lagrangian variables r, theta, phi, and chi. The interesting result is found that the applied force lifts the gyro and also changes its nutations and precessions. The applied force can be generated by an applied torque as in the Laithwaite and Shipov experiments. The dynamics are far too complicated to solve by hand but can be solved by computer to give a large amount of information. Eq. (10) is a simple transformation from frame (1, 2, 3) to frame (X, Y, Z).


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