A method of truncated characteristic equations for studying the stability of nonlinear periodic oscillations

摘要

Technique for studying the stability of nonlinear oscillations obtained by the harmonic balance method without the allowance for slow variations in amplitudes is developed the principles of truncation of the general characteristic equation describing an oscillatory system are formulated. Using these principles, the order of the truncated determinants representing the functional kernel of the system of partial characteristic equations is determined. The problem of determining and eliminating the false roots of the characteristic deter- minants is formulated and solved.