Rigid Body Dynamics - Part II

[Zenshin]

Hello again! About my last problem (cone principal moments of inertia around top vertice), I´ve found the main moments of inertia, but I did so by integrating the moments of inertia dI o a disk rotaing about it´s diameter (1/4 ML^2, by table), and found the correct answer. But I have done this by the way we did it in Basic Physics 1... in Classical Mechanics I, I think there´s a way in which you use "proportion factors" and find the moments of inertia like Ixx =M(Ky x Lambda-y + Kz x Lambda-z), but i could apply this method...Still, I haven´t figured out how to find a h/a (height / base radius) of that cone in which every axis passing through the vertice v is a principal axis... Somehow, I think it´s a eigenvalue and eigenvector problem of the Inertia tensor... Oh, and by the way, does anyone know how to find the moment of inertia of that disk, about it´s diameter?? I got the value from a table, since I could not find the answer myself...(tried something similar to the spherical moment of inertia by integrating a cascade of disks....didn´t work as well with a cascade of bars for the disk though...)


Thanks in advance!