Stabilizing skateboard speed-wobble with reflex delay.

A simple mechanical model of the skateboard-skater system is analysed, in which the effect of human control is considered by means of a linear proportional-derivative (PD) controller with delay. The equations of motion of this non-holonomic system are neutral delay-differential equations. A linear stability analysis of the rectilinear motion is carried out analytically. It is shown how to vary the control gains with respect to the speed of the skateboard to stabilize the uniform motion. The critical reflex delay of the skater is determined as the function of the speed. Based on this analysis, we present an explanation for the linear instability of the skateboard-skater system at high speed. Moreover, the advantages of standing ahead of the centre of the board are demonstrated from the viewpoint of reflex delay and control gain sensitivity.

Contact patch memory of tyres leading to lateral vibrations of four-wheeled vehicles.

It has been shown recently that the shimmy motion of towed wheels can be predicted in a wide range of parameters by means of the so-called memory effect of tyres. This delay effect is related to the existence of a travelling-wave-like motion of the tyre points in contact with the ground relative to the wheel. This study shows that the dynamics within the small-scale contact patch can have an essential effect on the global dynamics of a four-wheeled automobile on a large scale. The stability charts identify narrow parameter regions of increased fuel consumption and tyre noise with the help of the delay models that are effective tools in dynamical problems through multiple scales.