About the definition of a nonlinear inductance in static and dynamic regimes

The integral relations and integral-differential equations that take into account the influence of the magnetic shields (magnetic) inductance have been obtained. The non-linear magnetic materials with hysteresis and without it, and approximation of nonlinear materials and inductors have been considered. It is shown that for hysteresis we should use the nonlinear equation for the magnetization. The establishment of oscillations in a chain with the simplest approximation of a nonlinear inductance are reviewed. The effect of nonlinear magnetic shielding on inductance of radioreactor electric vehicle as depending on current and frequency are estimated.