Plans for UFT368: Lagrangian description of spinning top

This looks like a good system and could be developed for Section 3 of UFT368. For Sections 1 and 2 I am thinking of developing UFT270 for the symmetric top with one point fixed. Both methods combined should give plenty of interesting results with which to compare with the experimental data by Laithwaite and Shipov.

Lagrangian description of spinning top

I remember having modeled the Lagrangian for a rotating wheel some years
ago. This example is sometimes described in mechanics books. The wheel
(or rotating ring) mass can be considered as a mass parameter m and a
rotation angle alpha. So there is only one Lagrangian coordinate
required for this type of rigid body. This can be inserted into the 3D
motion in spherical coordinates, see attached sketch. The radius
coordinate r is constant, there are actually 2 constant radii R1 and R2.
The Lagrangian coordinates are theta, phi and alpha. One has to set up
the coordinate transformation from alpha to the lab system (sperical
coordinate system). Then the kinetic energy can be computed. The
gravitational force was already set up in paper 367. An external torque
works on the angle phi which should be easy to introduce because of the
usage of polar coordinates.

Horst

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: