• DocumentCode
    1406529
  • Title

    The x¿n-x Plane for Analysis of Certain Second-Order Nonlinear Systems

  • Author

    Deekshatulu, B.L.

  • Author_Institution
    Indian Institute of Science, Bangalore, India.
  • Volume
    82
  • Issue
    69
  • fYear
    1963
  • Firstpage
    315
  • Lastpage
    317
  • Abstract
    Analysis of certain second-order nonlinear systems, not easily amenable to the phase-plane methods, and described by either of the following differential equations x¿n-2¿+ f(x)x¿2n+g(x)x¿n+h(x)=0 ¿+f(x)x¿n+h(x)=0 n≫0 can be effected easily by drawing the entire portrait of trajectories on a new plane; that is, on one of the x¿n¿x planes. Simple equations are given to evaluate time from a trajectory on any of these n planes. Poincaré´s fundamental phase plane x¿¿x is conceived of as the simplest case of the general x¿n¿x plane.
  • Keywords
    Automatic control; Books; Control systems; Differential equations; Jacobian matrices; Nonlinear control systems; Nonlinear systems; Servomechanisms; Stability; Time varying systems;
  • fLanguage
    English
  • Journal_Title
    Applications and Industry, IEEE Transactions on
  • Publisher
    ieee
  • ISSN
    0536-1524
  • Type

    jour

  • DOI
    10.1109/TAI.1963.5407797
  • Filename
    5407797
    • Link To Document
    https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=1406529