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This paper deals with estimating the lateral stability region of a nonlinear 2 DOF vehicle via Lyapunov Second Method and the non-Lyapunov methods of tangency points and trajectory reversal. The nonlinearity of the model is incorporated in an analytical expression for the lateral tire force. It is shown that the derived analytical expressions for equilibrium points defines the outer limits of the stability region.

This paper presents the dynamical equations of motion governing a six degrees-of-freedom mathematical model of a three-wheeled all-terrain vehicle/rigid-rider system. The parameter values associated with two commercially available three-wheeled all-terrain vehicles, a 1980 Honda ATC 110D and a 1980 Kawasaki KLT 200, are presented. In addition, tire properties such as non-rolling vertical stiffness, cornering stiffness and damping ratio for a 22×11-8 Ohtsu tire and a 22×11-8 Goodyear tire are given. These parameter values are used to simulate the motions of the vehicle/ rider system with the results presented in Part II (1)*

This paper is the second in a series on three-wheeled all-terrain vehicles and investigates the handling and ride characteristics of the six degrees-of-freedom mathematical model of a vehicle/rigid-rider system with no suspension. This vehicle/rider system was simulated over three different bump profiles of rectangular, parabolic and sinusoidal shapes. The results show that a light vehicle/rider system equipped with a set of stiff tires has the poorest handling and ride characteristics whereas a heavy vehicle/rider system equipped with a set of soft tires has the best handling and ride characteristics. It was also shown that, for the particular profiles selected, a longer ramp-like bump profile disturbed the vehicle/rider sytems significantly more than a shorter length bump profile.

Several new mathematical models of a rider ATV system are developed. These new models allow the ATV to have either three or four wheels, the rider to be placed at any orientation relative to the vehicle, and the ATVs wheels to rotate. These models are used to investigate the simulated motion of an ATV system over a bump profile. For each model, overturning stability plots are generated as a function of the rider's side lean angle and the vehicle's initial velocity. These results show that the four-wheeled ATV system is more stable than the three-wheeled ATV system over the bump profile. In addition, the inclusion of wheel rotation only slightly improves the overturning stability of the ATV system and this improvement occurs only at high vehicle speeds.

In this paper fundamental analytical results for automobile lateral stability are developed. Specifically, the linear two degree-of-freedom, fixed steering control, front wheel steer and four wheel steer automobiles with a time lagged lateral tire force model is employed in the analysis. The stability conditions are derived using Routh Hurwitz criterion and Lyapunov’s method. The results are mainly algebraic in nature and examples are given demonstrating potential problems of front wheel and four wheel steering vehicles due to the time lag in the tire’s lateral force.