Yes it is possible, but its more complicated. I'm not a physicist. My skills in Mathematica are average.
If you want an answers, then write a new post(discussion).
Thank you, Mariusz, keep the good posts coming!
To response see above.
Your contributions are impressive, Mariusz! You must be an expert in dynamics and well informed about the rotational motion of all sorts of objects! This brings me to a demonstration I am hopelessly trying to get right. About the rolling of a marble inside a bowl. Attached is a demonstration I made some time ago. I know it dies not look right and the rotations of the marble are not consistent with experience. Maybe you can have look at it or get me on the right track. Or maybe yo know a publication that has the correct equations of motion?
The solution to this problem was not so hard .The required knowledge can be found on the Internet but In this case I myself solved.
You could say that your equation with a good approximation is correct . Details in the file. And then there's one thing I'm not an expert . Only an engineer.