Discussion of 368(7)

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.

To: EMyrone@aol.com
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).

Horst

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.

Advertisements
  1. No trackbacks yet.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

%d bloggers like this: