Periodic motions of the essentially nonlinear self-oscillation systems governed by Rayleigh's and Van-der-Pol's equations are constructed and studied. On the basis of the Lyapunov ? Poincare method combined with an accelerated convergence numerical method and continuation with respect to a parameter, the period and the initial velocity that correspond to self- sustained oscillations are calculated for small and moderately large values of the feedback gains. The phase trajectories and the limit cycles are constructed with a guaranteed accuracy. Qualitative features of the self-sustained oscillations that appear as the self-excitation coefficients increase are discovered. A comparison of the behavior of both oscillators is given. The results of the numerical analysis of periodic solutions of Rayleigh's equation are compared with the already available solutions in the quasi- linear approximation.
|
