Self-sustained oscillations of Rayleigh and Van der Pol oscillators with moderately large feedback factors

✍ Scribed by L.D. Akulenko; L.I. Korovina; S.A. Kumakshev; S.V. Nesterov

• Book ID: 104142388
• Publisher: Elsevier Science
• Year: 2004
• Tongue: English
• Weight: 570 KB
• Volume: 68
• Category: Article
• ISSN: 0021-8928
• DOI: 10.1016/s0021-8928(04)90023-8

✦ Synopsis

Periodic motions of essentially non-linear self-sustained oscillatory systems, described by Rayleigh and Van der Pol equations, are constructed and investigated. The period and initial value of the velocity of the system, which determine the self-sustained oscillations of the oscillators for small and moderately large values of the feedback factors, are calculated by the Lyapunov-Poincar6 method using a developed accelerated-convergence algorithm and a continuation with respect to a parameter. The trajectories and limit cycles are also constructed with a guaranteed relative and absolute error. The qualitative features of the self-sustained oscillations due to an increase in the self-excitation factors are established and the oscillators are compared. The results of a numerical investigation of periodic solutions of the Van der Pol equation are compared with familiar solutions.