Bifurcation analysis of static stability of a tractor-semitrailer under circular motions

This paper analyses a general qualitative depiction of changes in the configuration of the non-linear model of a tractor-semitrailer with excessive turnability under stationary circular motions within a broad range of control parameters, such as the longitudinal velocity of motion and angle of rotation of the wheels of the controlled unit. It allows us to foresee the jackknifing effect and to estimate the conditions necessary for safe travel. The proposed analysis combines the transparent geometric approach to analyse the configuration of a tractor-semitrailer, which was developed earlier by J.P. Pauwelussen, and the ability to investigate real bifurcations of the non-linear equation of handling and the non-linear equation of folding angle tractor-semitrailer analytically. Based on this approach, we obtain new analytical dependencies that determine the boundaries of divergent loss of stability of the entire manifold of stationary states of a tractor-semitrailer model and estimates of the maximum values of the angle of folding under different values of the vehicle's longitudinal velocity. This is achieved without the prior determination of the manifold of stationary states itself.