External Torque on a Gyro with One Point Fixed

This could be done in various ways, and the powerful code applied to solve the differential equations. I can set up the general equations and you can match them to the torque used by Shipov. In the meantime I can experiment with different potentials to model the effect of orbital motion on nutation and precession, and vice versa.

To: EMyrone@aol.com
Sent: 08/02/2017 12:08:04 GMT Standard Time
Subj: Re: 370(1): Orbital Motion of the Asymmetric Top

In particular it would be good if the effect of an external torque on a gyro fixed at one point could be handled in paper 370. This is important for describing the Russian experiments.
I am inspecting now the dumbbell model, freely flying in a graviational field.
Horst

Am 07.02.2017 um 10:30 schrieb EMyrone:

This note makes some remarks on UFT369 and sets up the usual lagrangian (2) used in a textbook such as Marion and Thornton. This lagrangian assumes that the translational and rotational kinetic energies are independent, so the problem reduces to solving independently the set of equations (8) to (10) and the set of equations (12) to (15). This means that the nutations and precessions of the symmetric top do not depend on its orbital position, e.g. they are the same at aphelion and perihelion. This theory is too simple to describe the Milankowitch cycles, so a more general five variable theory is needed. One way of developing this is to assume that the potential energy is in general a function of all five variables, and is no longer central, i.e. is no longer a function only of r. The mathematics of this note are examples of Cartan geometry, and insight which allows a great deal of development in future. Euler was the first to devise the idea of principal moments of inertia in 1750, and the idea is used in far infra red spectroscopy – rotational spectra of molecules.


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