Equations for sliding/rolling symmetric top

[James_Frogan]

Homework Statement

I am attempting to derive the equations of motion for a sliding/rolling (either case or both cases) symmetric spinning top that rises under the influence of sliding/rolling friction. This is a 6 degree of freedom system with the 3 Euler angles and 3 xyz directions (although the tip of the top is constrained to contact with the surface).

I hope to use Lagrange's equations, but haven't found any journal article/paper showing that this is possible. Am I headed down a dead end?

Homework Equations

Lagrangian mechanics
Sliding/Rolling friction
There are several alternatives, Routhian reduction, etc.

The Attempt at a Solution

The derivation for the fixed tip case is fairly simple, I'm wondering if it can be extended to 6DOF case.

 

[BigJDubs]

I'm not sure if Lagrange's equations would be suitable for this problem. Routhian reduction could be a possible approach, but I'm not quite sure how to go about it. Any help or guidance would be greatly appreciated!