Models for Tilting Body Vehicles

The models seen in the previous chapters dealt with vehicles that maintain their symmetry plane more or less perpendicular to the ground; i.e. they move with a roll angle that is usually small. Moreover, the pitch angle was also assumed to be small, with the z axis remaining close to perpendicular to the ground. Since pitch and roll angles are small, stability in the small can be studied by linearizing the equations of motion in a position where θ = ø = 0.

Two-wheeled vehicles are an important exception. Their roll angle is defined by equilibrium considerations and, particularly at high speed, may be very large. To study the stability in the small, it is still possible to resort to linearization of the equations of motion, but now about a position with θ = 0, ø = ø₀, where ø₀ is the roll angle in the equilibrium condition. An example of this method is shown in Appendix B, where the equation of motion of motorcycles is discussed.