The mechanism of stability loss for the rectilinear motion of a rail wheelset (Q2754684)

Rectilinear motion of a wheelset becomes instable in the Lyapunov sense when the velocity exceeds some critical value. For improving ride performance of a carriage or locomotive frame \textit{C. P. Keizer} suggested to join the wheelset by two longitudinal and two transverse elastic elements. In his work, the problem was studied numerically. In the present paper, an analytic expression for the critical velocity was found by using technique of Lyapunov functions. Classification of forces by their mathematical structure is given, mechanism of stability loss is examined. A nonlinear system of ordinary differential equations for the lateral displacement and the angle of wagging is derived and a linear approximation of equations of perturbed motion is obtained. Conclusions regarding loss of stability of the studied system are made.