**1.2 - Definition of rods T1 and T2**
**T1** is an inertial rod.

At t=0 in

**S**,

**T1** is tangent to wheel element

**P**, and moving with the same velocity as

**P**.

**T2** is a rod permanently attached to the wheel at

**P**.

At t=0 in

**S**, the location of

**T2** coincides with the location of

**T1** as illustrated:

**T2** moves rigidly in

**S** in such a way that it remains tangent to the wheel at

**P** at all times.

For example, at $$t = \pi/(2\omega)$$ in

**S**,

**T2** has moved around the wheel with

**P**, while

**T1** has moved inertially, as illustrated:

Does that make sense? There is no coordinate dependence in that description that I can see, but here are the equations of motion in vector form anyway:

**Equations of motion**
$$\vec{v_P}(t)$$ is the velocity of wheel element

**P** at time t in

**S**.

Let $$\vec{P}(t)$$ denote the position vector of

**P** at time t in

**S**.

Let $$\hat{P_t}(t)$$ denote the unit displacement vector tangent to wheel element

**P** in

**S** at time t.

Let $$\vec{T_1}(t,l)$$ denote the position vectors of the elements of rod

**T1** at time t in

**S**, where $$l$$ is distance along the rod from the element that was in contact with

**P** at t=0.

Let $$\vec{T_2}(t,l)$$ denote the position vectors of the elements of rod

**T2** at time t in

**S**, where $$l$$ is distance along the rod from

**P**.

Thus:

$$\vec{T_1}(t,l) = \vec{P}(0) + l\hat{P_t}(0) + t\vec{v_p}(0)$$

$$\vec{T_2}(t,l) = \vec{P}(t) + l\hat{P_t}(t)$$