# final - Physics 821 Dr. Herbst Spring Quarter 2005 FINAL...

This preview shows pages 1–2. Sign up to view the full content.

Physics 821 Spring Quarter 2005 Dr. Herbst FINAL EXAMINATION WEDNESDAY, JUNE 8 9:30 – 11:18 AM 100 POINTS 1) (25 points) The Lagrangian for the torque-free rotation of a rigid symmetric top around its center of mass is given, in terms of Eulerian angles, by the expression L = 1 2 I 1 ( ˙ f 2 sin 2 q + ˙ q 2 ) + 1 2 I 3 ( ˙ cos + ˙ y ) 2 where the two equal moments of inertia are designated I 1 . a) (15 pts) Determine decoupled expressions for the rates of precession ( ˙ ) and spinning ( ˙ ) in terms of constants of the motion and the nutation angle q . Is either of these rates constant? If so, under what conditions? b) (10 pts) Use your results to a) to get expressions for w 3 and w 1 2 + w 2 2 . Discuss the meaning of your answers. In particular, try to answer whether or not the top nutates. Remember that w 1 2 + w 2 2 was shown to equal a constant A 2 when we used Euler’s equations. 2) (35 points) a) (15 pts) Find the eigenvalues and normalized eigenvectors for the problem: L = 1 2 m ( ˙ x 1 2 + ˙ x 2 2 ) - 1 2 kx 1 2 - 1 2 kx 2 2 - 1 2 k ( x 2 - x 1 ) 2 where the x

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 06/13/2011 for the course PHYSICS 821 taught by Professor Eric during the Spring '07 term at Ohio State.

### Page1 / 2

final - Physics 821 Dr. Herbst Spring Quarter 2005 FINAL...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online