energy must be extracted from the forward motion of the wheelset. The outer wheel velocity is given by: The kinetic energy is: for the inner wheel it is where is the mass of both wheels. The increase in kinetic energy is: The motion will continue at constant amplitude as long as the energy extracted from the forward motion, and manifesting itself as increased kinetic energy of the wheel set at zero yaw, is equal to the potential energy lost by the lowering of the axle load at maximum yaw. Now, from the kinematics: but The translational kinetic energy is The total kinetic energy is: The critical speed is found from the energy balance: Hence the critical speed is given by This is independent of the wheel taper, but depends on the ratio of the axle load to wheel set mass. If the treads were truly conical in shape, the critical speed would be independent of the taper. In practice, wear on the wheel causes the taper to vary across the tread width, so that the value of taper used to determine the potential energy is different from that used to calculate the kinetic energy. Denoting the former as , the critical speed becomes: where is now a shape factor determined by the wheel wear. This result is derived in Wickens (1965) from an analysis of the system dynamics using standard control engineering methods. Limitation of simplified analysis The motion of a wheel set is much more complicated than this analysis would indicate. There are additional restraining forces applied by the vehicle suspension and, at high speed, the wheel set will generate additional gyroscopic torques, which will modify the estimate of the critical speed. Conventionally a railway vehicle has stable motion in low speeds, when it reaches to high speeds stability changes to unstable form. The main purpose of nonlinear analysis of rail vehicle system dynamics is to show the view of analytical investigation of bifurcation, nonlinear lateral stability and hunting behavior of rail vehicles in a tangent track. This study describes the Bogoliubov method for the analysis. Two main matters, namely assuming the body as a fixed support and influence of the nonlinear elements in calculation of the hunting speed, are mostly focused in studies. A real railway vehicle has many more degrees of freedom and, consequently, may have more than one critical speed; it is by no means certain