Hi all

I'm looking for a Lyapunov function to determine stable and unstable areas on a vehicle, using Phase Portrait analysis. Statable variables are Side Slip Angle (beta) and Yaw Rate (r). I've already tried some functions such as V=beta^2+r^2 or V=(beta+r)^2, but I'm not achieving the results I expect (some may get close but don't clearly show the unstable areas). Could somebody help? I'm using the 2DOF bicycle model and Pacejka equations for the tyre. Equations are basic lateral forces equilibria and moment equilibria around the vertical axis:

beta_dot=(Fyfront+Fyrear)/m*Vx-r and

r_dot=(a*Fyfront+b*Frear)/Izz

being:

Fyfront and Fyrear: Lateral forces on the front and rear axle respectively

m=Vehicle mass

Vx=Vehicle forward velocity

a and b: Distance between front and rear axle respectively to the CoG of the vehicle

Izz= Rotational inertia for vertical axis

thanks a lot

Andoni