Please derive the dynamics of an infinitely thin rolling tire.

The world coordinates are Z upwards, Y forwards, and X to the right.
The tire is contacting the ground at (x,y) expressed in world coordinates.
I wnat the contact coordinates to evolve (e.g., track the rolling footprint
across the ground).
There is no translational slip at the contact point,
but there is rotational slip at the contact point and a rotational
friction torque tf around a vertical axis applied at the contact point.

The tire in the zero position has its axle parallel to the X axis,
and the tire's body coordinates are aligned with the world coordinates.
The plane of the tire is perpendicular to the axle and is coplanar
with the world and body Y-Z planes in the zero position.

The orientation of the tire is described with three angles: roll (r),
pitch (p), and yaw (y).
Roll is the angle of the plane of the tire with respect to vertical,
so in the zero position with the tire on its rim with its axle parallel
to the X axis, the roll is zero.
The pitch of the tire is the amount of rotation about the axle of the tire
from the zero position.
The yaw of the tire is a rotation about the axis perpendicular to both
the wheel axle and the roll axis of the wheel.

The circularly symmetric infinitely thin tire has a mass Mw, center of
mass at its geometric center, and moment of inertia tensor Iw.
The radius of the wheel is Rw.
Torques can be applied about the pitch (tp), roll (tr), and yaw (ty) axes
expressed in the body coordinates of the tire.
I want to express angular velocity (wx, wy, wz) of the tire in 
body coordinates.  Gravity acts in the downwards Z direction.

I would like to see detailed derivations of the inverse dynamics of
the tire solving for tp, tr, ty given x, y, r, p, y, wx, wy, wz, 
accelerations wxd, wyd, and wzd, the wheel radius Rw,
the inertial parameters Mw and Iw, and the friction torque tf.
I would like to see detailed derivations of the energy of the tire
in terms of its position, velocity, acceleration, orienation, angular
velocity, angular acceleration, wheel radius Rw, and inertial parameters
Mw and Iw.
I would like executable C programs to compute the inverse dynamics and
energy, based on these derivations, with the derivation information included
as comments in the programs.