On verification of stability of periodic oscillations in nonlinear systems

A method for verification of stability of periodic oscillations in nonlinear systems is proposed. The main oscillation is represented in the exponential form and is substituted into the initial differential equation. Then the approximating differential equation with respect to the same exponent is taken. The terms representing higher than the first-order derivatives are omitted in the corresponding operator equation. The real and imaginary parts of this simplified operator equation are separated and give two nonlinear differential equation of the first order for the amplitudes of the main oscillation. These equations can be used for calculation of transients. The differential equations of variations obtained from the equations of the amplitudes are used for verification of stability of the main oscillation.