Non-Local Methods for Pendulum-Like Feedback Systems

0 are already deecribed by I. Newton (116]. However it was 250 years later that F. Tricorni (147] carried out the first non-local qualitative investigation of equation (0.1) with arbitrary o ~ 0 and "'{ ~ 0. It was proved by F. Tricorni that any solution of (0.1) with o 0 corresponds either to a rotatory motion or to a damped oscillatory motion. Moreover, he showed that in the non-trivial case "'! :::; 1 there exists a bifurcation value ocr("'!) corresponding to a separatrix-loop, i.e. to a double-asymptotic to a saddle-point trajectory. For o ocr("'') global asymptotic stability takes place, i.e. every motion is a damped oscillation. The papers of F. Tricorni became familiar immediately.

List of contents

Systems with Multiple Equilibria.- Pendulum-Like Systems.- Invariant Cones.- The Bakaev-Guzh Technique.- The Method of Non-Local Reduction.- Circular Solutions and Cycles.- Synchronous Machines Equations.- Integro-Differential Equations.- Cycle Slipping in Phase-Controlled Systems.- Discrete Systems.

Product details

• Authors: Gennadij Leonov, Volke Reitmann, Volker Reitmann, Vera Smirnova, Vera B Smirnova, Vera B. Smirnova
• Publisher: Vieweg+Teubner
• Languages: German
• Product format: Paperback / Softback
• Released: 14.11.2013
• EAN: 9783663122623
• ISBN: 978-3-663-12262-3
• No. of pages: 242
• Illustrations: VII, 242 S.
• Series: Teubner-Texte zur Mathematik; Teubner-Texte zur Mathematik
• Subject: Natural sciences, medicine, IT, technology > Technology > Miscellaneous