Downhill Motion of the Skater-Skateboard System

Abstract

The lateral instabilities of vehicles are well-known phenomena, see for example, the shimmy motions of bikes, motorbikes or the steered wheels of cars. Another interesting phenomenon is the snaking motion of the skateboard-skater system that is analyzed in this study. A mechanical model of the downhill skateboarding is constructed in order to consider the effect of the slope angle on the stability. The equations of motion are obtained with the help of the Gibbs-Appell method. The linear stability analysis of the rectilinear motion is carried out analytically using the Routh-Hurwitz criterion. The influence of different realistic parameters of the skater and the board are investigated. A critical position of the skater on the board also is determined.