Road vehicles travelling with time-dependent speed: theoretical study on the directional stability

In this paper, directional stability of road vehicles travelling at time-dependent forward velocity is investigated. The dynamical behaviour of the system is governed by a set of linear ordinary-differential equations with time-varying coefficients. A simple two degrees of freedom (DOF) model is considered, in order to better understand the effects of such a perturbation on the well-established bicycle model, which is frequently used in the literature as a first approach to get useful physical insights on vehicle dynamics. Numerical simulations show significative differences with respect to the prediction of the stability analysis in the case of constant forward speed. A moderately large variation on the forward velocity, indeed, can stabilise the vehicle which is statically unstable. Stability maps are obtained by means of the Floquet theory, with the aim to shed light on the modified vehicle dynamics. A final discussion is provided, which leads to outline the possible practical applications of the present investigation, together with future comprehensive studies.