Unity, Duality & Trinity

In a world without imperfections and without gravity a spinning coin would remain standing on its edge, but as we build imperfect objects and enact imperfect actions, the coin will fall in time. The way in which it falls is of interest. The inevitable skew causes torque, rotational force, which is then acted on by gravity. Gravity’s impact on torque changes the tilt of the axis of rotation (theta) and this is known as precession.

Suppose a coin is rotating clockwise (+x). Gravity exerts its force (-z) which combines with the (+x) velocity in the xy plane. Rather than the gravitational pull being seen as an immediate downward motion, it is seen 90 degrees ahead creating a diagonal orbit and a new axis of rotation (ws).

In the example of Euler’s disk, the greater the angle of precession from the ground plane, the smaller the range of motion on the xy plane. As the angle of precession decreases, it spins more slowly, but the rate of precession increases.

The spin slows because of friction. The proportion of gravitational torque increases as the disk’s center of gravity extends further from its contact point with the ground and there is more leverage. The rate of precession increases because as the angle of precession decreases, more of the disk’s edge makes contact with the ground plane and the greater the axial range of motion on the xy plane.