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The article sets out the methodology of the study of a rigid mathematical model describing locomotive wheel and rail interaction, taking into account the hypothesis f. Carter. On the basis of the application of the theorem N.A. Tikhonova derived the differential equation for determining the rate of slippage of wheel pair on Rails. Determine the time dependence for the establishment of a process of kinematic slippage of wheel pair on Rails from the wheel speeds and locomotive, from inertial characteristics of trains and the wheel, as well as the coefficient of creep, annexed to the torque of wheel pair and the State of the surfaces of the Rails.