Consider a symmetric, non-nutating precessing top with one point fixed (the tip if you will). It's symmetry axis is at an angle $\theta$ to the vertical and it steadily precesses at some angular velocity $\Omega$. The top's angular momentum component along its symmetry axis is:
Now, given these conditions I wanted to see if the mass could be obtained. Note that Gravity is acting on the top. I found an expression by taking the time derivative of the angular momentum and equating that to the torque induced by gravity. My answer is:
Where $\ell$ is the distance from the fixed point to the center of mass. However this seems a bit strange because all the explicit dependence on the angle $\theta$ disappeared. My question is, does this make sense, and if so why? Or is my answer garbage? I'm thinking it has something to do with the fact that the initial assumptions make the top unable to nutate, and the $\theta$ dependence is somehow implicit.