Elucidating vehicle lateral dynamics using a bifurcation analysis

Issues of stability and bifurcation phenomena in vehicle lateral dynamics are presented. Based on the assumption of constant driving speed, a second-order nonlinear lateral dynamics model is obtained. Local stability and existence conditions for saddle-node bifurcation appearing in vehicle dynamics with respect to the variations in front wheel steering angle are then derived via system linearization and local bifurcation analysis. Bifurcation phenomena occurring in vehicle lateral dynamics might result in spin and/or system instability. A perturbation method is employed to solve for an approximation of system equilibrium near the zero value of the front wheel steering angle, which reveals the relationship between sideslip angle and the applied front wheel angle. Numerical simulations from an example model demonstrate the theoretical results.