Derivation of linear single-track truck-dolly-semitrailer model with steerable axles

We consider a linear single-track model of a truck-dolly-semitrailer by deriving Lagrange's equations with the quasi-coordinates chosen as the body fixed longitudinal and lateral velocity of the truck, vx1 and vy1, respectively, the yaw angle of the truck and the articulation angles of the dolly and the semi-trailer. The linear analysis and simulations are carried out with a constant longitudinal velocity of 80 Kph for the passive vehicle, i.e. no steering on the dolly or semitrailer. The analysis shows an increase in yaw rate gain for the dolly and semitrailer, compared to the truck, for frequencies around 0.4 Hz on the truck steering angle. That is, we have a yaw rate RWA higher than 1 when for frequencies around 0.4 Hz. We also observe a lateral acceleration gain, between 0.1 and 1 Hz, for the dolly and semitrailer. Moreover, the phase angle has a higher frequency dependence for the dolly and semitrailer both for yaw rate and lateral acceleration. Time simulations shows that the dolly and semitrailer experience a time delay and an overshoot when the vehicle combination is subjected to various steering angle maneuvers. This indicates that the vehicle combination is not as stable as the truck alone.