Understanding the Equations Behind Car Dynamic Steering Systems

[ahhm208]

Hi,
I have these equations which represent the car steering angles and velocity, but I could not understand how do the operate.They are used for continus turning motion without keeping track of the car angle Beta. I would like some hints if anybody is familiar with them or have any other similar equations or references:

PSI=arcsin( (v/d)*sin(Tyre Angle) );
course=Beta+PSI;
Gamma=Tyre Angle+course;

B=L*cos(Beta)+v*cos(Gamma)-L*cos(course);
C=cos(course);

rear velocity=B/C;

where
L : length between tyres.
Beta: is the slip angle( car angle)
PSI:is the angle below of Beta

 

[Navin A S]

Tyre Angle: is the angle of the tyred : is the distance between tyresThese equations are used to calculate the steering angles and velocity of the car. The first equation calculates the PSI, which is the angle between the car angle Beta and the angle of the tyre Tyre Angle. Then, the second equation calculates the course angle which is the sum of Beta and PSI. The third equation calculates the Gamma, which is the sum of the tyre angle and the course angle. The fourth and fifth equation are used to calculate the rear velocity of the car which is the difference between the length of the car multiplied by the cosine of Beta and the velocity multiplied by the cosine of the Gamma minus the length of the car multiplied by the cosine of the course angle. The sixth equation simply calculates the cosine of the course angle.Finally, the rear velocity is calculated by dividing B with C. Hope this helps.