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It is shown that dynamic systems, «rolling stock - way» due to the unevenness of the path on length should be described by ordinary differential equations with variable coefficients, the method of analyzing differential equations with constant, variable and random coefficients describing the movement of electric locomotive nodes when they move along an uneven path. In the transition to a new paradigm, we can talk about areas of dynamic instability, which in the case of simple parametric resonances develop near critical frequencies, but this is not one specific point, but a zone that expands with increasing coefficients of parametric excitation. In addition, the presence of friction in the system does not guarantee the limitation of resonant amplitudes. The effect of parametric arousal factors on the width of the dynamic instability zone has been established. There are many other features in the behavior of differential equations with variable coefficients, so it is impossible to replace the action of unevenness with some equivalent geometric irregularity, since at this moment there is no exact solution to the problem with which to compare the results of approximate mathematical models.

The article deals with such important concept as the resonance to three cases: when rolling stock is described by a system of linear differential equations with constant coefficients, when the mathematical model of rolling stock represented a nonlinear system of differential equations, and when in the latter we take into account the multiplicative disturbance from railway, namely its non-equal-elasticity between sleepers. In this case, speak properly and correctly is not about a particular value of RMS-velocity, but on parametric instability areas.

Explores the impact of truly existing longitudinal non-elastic railway track caused by the presence of sleepers and other factors on the vertical dynamic of vehicle. Formulas to determine the bounds of simple combinational and parametric resonances is obtained. Areas of dynamic instability of electric locomotive EP2K is builted.

The article is devoted to the accounting problem of longitudinal non-equal-elasticity of railway track which led to forced vibrations for non-spring mass of rolling stock are interacting with multiplicative perturbation, that is increasing the amplitude of the bouncing wheel pair, or reducing it. This depends on the phase relationship between these influences .

The article devoted to results of the longitudinal multiplicative perturbation effect from railway track in relation to rolling stock.There is the technique for finding of difference type Raman resonances areas,which based on the theory of division in slow and fast components for motion of dynamic system.It proves a fact that the RMS-velocity for motion of the train is not a specific numerical value,but that is an area for which the width depends on the multiplicative factor driving

The article proposes a method for increasing the efficiency of power supply systems for non-tangible consumers due to quadratic accumulation of electric energy on reactive elements in the frequency-beating mode. The proof of the energy efficiency of the beating regime in comparison with the full resonance regime with respect to the implementation of quasiresonance pulsed power supplies is given. The article also deals with the choice of the optimal beat frequency by the criterion of the maximum ratio of the accumulated energy on the reactive elements of the circuit to the one expended from the primary source.