On the instability of a car in the vertical plane under rectilinear motion with friction forces taken into account

We consider the problem on the stability and instability of the equilibrium in the vertical plane for a wheeled vehicle performing a uniform rectilinear motion in the presence of rolling friction forces. We assume that the dependence of the rolling friction coefficients on the motion velocity is known and derive necessary and sufficient conditions on the system parameters under which such equilibria are stable.