Lagrange constraint mechanics problem

[DylanG]

http://img221.imageshack.us/img221/3754/capturetp.png

Just a simple question. I can see that for this to work I need:

T_rot = 1/5 ma²(thetaDOT + phiDOT)²

Just can't work out what phi has to do with rotational kinetic energy. I would have thought it would need to be simply the same thing but without the phiDOT term.

 

[diazona]

$\theta$ is the angular position of an identified point on the smaller sphere, measured with respect to the line joining the centers of the two spheres, right? Note that not only does $\theta$ change with time, but so does the orientation of that joining line, so you need to take that into account as well. That's where the $$\dot\phi$$ comes from.