The models seen in the previous chapters dealt with vehicles that maintain their symmetry plane more or less perpendicular to the ground; . 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 = φ = 0. Two-wheeled vehicles are an important exception. Their roll angle is defined by equilibrium considerations and, particularly at. | 31 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 . 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 6 fr 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 6 0 fr 0 where 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. Two-wheeled vehicles aside this condition also occurs when the body of the vehicle is inclined with respect to the perpendicular to the road this may be accomplished manually as in motorcycles or by devices usually an active control system that hold the roll angle to a value determined by a well-defined strategy. Vehicles of this type are usually defined as tilting body vehicles. The most common application of tilting body vehicles today is in rail transportation but road vehicles following the same strategy particularly those with three wheels have been built. Rolling may be controlled according to two distinct strategies by keeping the z-axis in the direction of the local vertical or by insuring that the load shift between wheels of the same axle vanishes. In the case of two-wheeled vehicles the latter strategy results in maintaining roll equilibrium The two strategies coincide G. Genta L. Morello The Automotive Chassis Volume 2 System Design 617 Mechanical Engineering Series Springer Science Business Media . 2009 618 .
