Abstract
The article considers the tasks associate with the study of dynamic processes of interaction between rolling stock and railways. Studies of the interaction of a wheel with a rail, fitting the vehicle into curves when modeling critical and emergency situations do not allow oversimplification of basic differential equations. And they should be based on exact nonlinear equations that take into account the entire set of geometric and kinematic relationships without simplification. An objective assessment dynamic characteristic of the vehicle can only be obtained by simultaneously taking into account both its vertical and horizontal irregularities. In order to determine boundaries of parametric resonance, article proposes method of generalized Hill’s determinants, the application of which is possible without taking into account small parameters.