# Precession of ellipsoid Question

1. May 31, 2007

### the keck

1. The problem statement, all variables and given/known data

A uniform symmetric ellipsoid (Mass M) has a large semi axis c and small semi axis a. A particle of mass m<<M is moving along a straight line parallel to the x-axis with speed v(i). Its y-coordinate is a/2 and its z-coordinate it c/2. After an inelastic collision, it sticks to the ellipsoid and then it (The ellipsoid) starts to move and rotate. One can assume the moment of inertia of the composite system equals to that of the ellipsoid.

Find the precession of the ellipsoid c-axis around direction of the angular momentum

3. The attempt at a solution

There are a couple of initial things I worked out:

- By linear momentum conservation, v(f)=m*v(i)/M

- The angular momentum of the composite system is L=M*v(f)*a + (2/5*M*a^2)*(v(f)/a) = 7/5*M*v(f)*a

- From what I guess, the ellipsoid rotates and precesses about the z-axis, but I'm still sort of learning precession, so I'm not sure how to go about doing this.

Thanks

Regards,
The Keck