The Equations and Their Properties

  • J. A. Richards
Part of the Communications and Control Engineering Series book series (CCE)


Differential equations with periodically varying coefficients appear in a number of forms, some of which are known by specific names. In this chapter these forms are identified and the general conventions adopted in this book are outlined. Whilst some are expanded upon in later chapters, the essential properties of the equations are also summarised, particularly those of importance in practical applications.


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References for Chapter 2

  1. 1.
    McLachlan, N. W.: Theory and application of Mathieu functions. Clarendon: Oxford U. P. 1947. Reprinted by Dover, New York 1964Google Scholar
  2. 2.
    Magnus, W.; Winkler, S.: Hill’s equation. New York: Wiley 1966zbMATHGoogle Scholar
  3. 3.
    Arscott, F. M.: Periodic differential equations. Oxford: Pergamon 1964zbMATHGoogle Scholar
  4. 4.
    D’Angelo, H.: Linear time-varying systems: Analysis and synthesis. Boston: Allyn & Bacon 1970zbMATHGoogle Scholar
  5. 5.
    Yakubovich, V. A.; Starzhinskii, V. M.: Linear differential equations with periodic coefficients, Vol. 1 and 2. New York: Wiley 1975. (Translation from Russian)zbMATHGoogle Scholar
  6. 6.
    Keenan, R. K.: An investigation into some problems in periodically parametric systems. PhD Thesis, Monash University Melbourne 1966Google Scholar

Copyright information

© Springer-Verlag Berlin, Heidelberg 1983

Authors and Affiliations

  • J. A. Richards
    • 1
  1. 1.School of Electrical Engineering and Computer ScienceUniversity of New South WalesKensingtonAustralia

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