*5.1. Determining the Position of Each Point Bk Relative to the Wheel-Fixed Reference Frame {O}*

The origin of the wheel-fixed reference frame {*O*} is at the wheel center *O*, where the *xz* plane is the rim center plane and the *y* axis is the wheel rotation axis (with the unit vector **e***ky*).

This can be done in the polar coordinate system shown in Figure 5b, where point *Bk* has coordinates (*r*0, *αk*). In each simulation step the angle *α<sup>k</sup>* of each point is measured from the thick horizontal line, clockwise.

At the beginning of the simulation (i.e., *i* = 0, *t* = 0 s) point *B*<sup>0</sup> has the polar coordinates (*r*0, *α*0) = (*r*0, 0) and the other points *Bk* have the coordinates (*r*0, *αk*), where:

$$a\_k = a\_k(t) = a\_{k-1} + \frac{d\_k}{r\_0} \text{ [rad]}, \ k = 1, \ldots, n. \tag{14}$$

This formula can be applied in the function Angular\_position\_of\_block() shown in Appendix A (*Code 1*), in section *Code 1*.
