Novel modeling of skidding effects on the nonholonomic motion of a vertical rolling disk

In this paper the motion of a simple vertical rolling disk in the presence of significant skidding effects is investigated. The nonholonomic constraints are adjusted to account for the skidding and two novel friction models are proposed that relate skidding in a wheel to the Lagrange multipliers associated with the kinematic constraints of that wheel. We study the motion of the disk under icy road conditions and to verify the correctness of our model, we compare it to one in the literature. We finally show how inputs that cause a zero net change in the position of the disk under ideal, no-skidding conditions generate a non-zero motion when skidding is significant.