Moment of Inertia Transfer

Hi Guys,

I've written a clutch model for my simulation based off a few papers I've read which basically deal with it as a state machine; that is there are two separate equations to integrate the motion when it is either locked or slipping. I'm interested to find out if this can be dealt with in the same equations of motion regardless of which state the clutch is in.

Currently when the clutch is slipping I integrate the input and output shafts separately with torque transferred between them based of the friction capacity of the clutch material. When it is locked, I integrate them as one system.

My main question revolves around how the moment of inertia is transferred between two rotating bodies that are in contact with each other. I'm assuming that as friction between the bodies increases, a quantity of inertia is both lost and gained from one another? Are there any formulae that deal with this situation? Let me know if that's clear