• DocumentCode
    1167010
  • Title

    Existence and uniqueness results for Lienard´s equations

  • Author

    de Figueiredo, Rui J.P.

  • Volume
    17
  • Issue
    3
  • fYear
    1970
  • fDate
    8/1/1970 12:00:00 AM
  • Firstpage
    313
  • Lastpage
    321
  • Abstract
    A new set of conditions for the existence and uniqueness of the periodic solution of the equation \\ddot{x} + f(x)dot{x} + g(x) = 0 (superscript dot = d/dt ) is given. Lyapunov-like functions are used in the derivation of the results. This permits the formulation of the existence and uniqueness conditions in a simple yet general way. The present conditions include those of Libnard and Levinson and Smith when particularized to the above equation. They also permit the inclusion of most of the cases of two-stroke oscillators covered by the author\´s previous theorems for equations of the above type. Periodicity results for the forced equation \\ddot{x} + f(x)x + g(dot{x}) = e(t) with e(t) periodic and bounded are also given.
  • Keywords
    Circuit theory; Automatic control; Error analysis; Feedback control; Finite wordlength effects; Laplace equations; Linear approximation; Linear systems; Nonlinear equations; Oscillators; Transient response;
  • fLanguage
    English
  • Journal_Title
    Circuit Theory, IEEE Transactions on
  • Publisher
    ieee
  • ISSN
    0018-9324
  • Type

    jour

  • DOI
    10.1109/TCT.1970.1083127
  • Filename
    1083127
    • Link To Document
    https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=1167010