single track model

1.  single track model (2 degree-of-freedom  linear ) :
A mathematical representation of a vehicle in which small steering and tire slip angles are assumed. In this instance the radius of curvature is assumed to be large and thus the left and right side tires are combined into a single front and single rear tire, like a bicycle. A linear tire is assumed, meaning that the tire slip angle remains small, typically below about three degrees. The two degrees of freedom for this model are lateral velocity and yaw rate

2.  single track model (3 degree-of-freedom linear ):
A mathematical representation of a vehicle with the same steering and tire assumptions as the 2 DOF model, but with an additional degree of freedom. the roll angle of the sprung mass was considered.

3. Bicycle Mode : single track model

4. CG  : vehicle center of gravity
5. Cα   : tire cornering stiffness (N/rad)
6. Cφ   : total roll damping (Nms/rad)
7. u      : longitudinal velocity (m/s)
8. v ,v'  : lateral velocity (m/s) , lateral acceleration (m/s2)
9. αf, r  : tire slip angle (rad)
10. δf   : front steer angle (rad)
11. φ    : roll angle (rad)
12. φ'   : roll velocity (rad/s)
13. φ''  : roll acceleration (rad/s2)