Physics 422 -- Fall 2006

Homework #7, due Wednesday Oct. 25 at beginning of class

1. [4pts]    Marion & Thornton problem 11.22

2. [4pts]    Marion & Thornton problem 11.27

3. [4pts]    Marion & Thornton problem 11.29.
Hint: You can't assume theta=0, because you want to allow it to fall. But you want to assume theta=0 is *possible*, which means that you should assume p_phi = p_psi.

4. [4pts]    Marion & Thornton problem 11.31. Hints: Kinetic energy and the square of the angular momentum are constants of the motion. You can use the given initial conditions to evaluate those constants. One of them is pleasantly simple. Using these results, you can change one of the three Euler equations into an equation that involves only one of the three variables omega_1, omega_2, or omega_3; and you can integrate that equation. Note that the angle between omega and the plane of the object is given by alpha -- that means that the angle between omega and the body z direction is (pi/2 - alpha).

5. [4pts]    Marion & Thornton problem 11.34.