On the statistical analysis of the motion of some simple two-dimensional linear vehicles moving on a random track☆

Abstract The influence of the length parameters—base length, idealized-tire spread and track-roughness spread—on the assumed “ride” criterion of some simple two-dimensional linear vehicles is examined. This examination is made under the assumption that the vehicles move with constant horizontal velocity on a weakly stationary random track in such a way that contact is maintained with the track throughout the motion. It is found that base length and track-roughness spread have a pronounced influence on the ride criterion throughout the range of interest in this paper. However, the idealized-tire spread only produces a marked effect on the ride criterion if the base length has been badly chosen. As the analysis is based upon second-order statistical properties, a knowledge of all of the joint probability distributions of the random track is not required.