• I. Andrianov
  • J. Awrejcewicz
  • L. I. Manevitch
Part of the Foundations of Engineering Mechanics book series (FOUNDATIONS)


A wide spectrum of references has been devoted to the averaging method [180, 592, 706]. Although the roots of the method come from pioneering works of H. Poincaré and B. Van der Pol, the kernel has been developed by the works of N. Krylov and N.N. Bogolyubov. In general, the averaging method uses splitting of fast and slow solution components. Assume that a solution to a certain problem has the form shown in Figure 8.1.


Average Method Power Series Form Duffing Equation Relaxation Kernel Hausdorff Formula 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • I. Andrianov
    • 1
    • 2
  • J. Awrejcewicz
    • 3
  • L. I. Manevitch
    • 4
  1. 1.KölnGermany
  2. 2.Pridneprovskaya State Academy of Civil Engineering and ArchitectureDnepropetrovkUkraine
  3. 3.Dept. of Automatics and BiomechanicsTechnical University LodzLodzPoland
  4. 4.N. N. Semenov Institute of Chemical Physics RASMoscowRussian Federation

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