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A mathematical model describing the dynamics of mechanical oscillatory systems «rolling stock train -railway track» in the vertical longitudinal plane of symmetry. Is equivalent to converting the design scheme. Linearization of nonlinear characteristics in ways. A model of the «generalized» track to assess the existing shock pulses from the joints of rails.

In this paper the authors propose to consider the peculiarities of making mathematical models of rolling stock and its dynamic behavior when driving on irregular resilience railway line in the longitudinal direction. We present a qualitative and empirical analyzes of longitudinal resilience railway railway. In conclusion, given the conclusion, on the basis of its proposed further consideration of mathematical aspects of the above solutions of systems of differential equations of motion of the rolling stock on irregular resilience way.