The Stability of Second Order Quadratic Differential Equations,

Abstract

In this paper a detailed study of the stability properties of the quadratic differential equation is undertaken. After observing that such systems can never be asymptotically stable the equilibrium states of the quadratic differential equation are classified in terms of the matrices G and H. Necessary and sufficient conditions for the stability of the origin are derived and constitute the principal contribution of this paper. Finally, these conditions are re-derived and elaborated using polar coordinates which allow a convenient classification of instability behavior. This exhausts the stability characteristics (in the sense of Lyapunov) of second order quadratic differential equations.

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Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1977
Accession Number
ADA049771

Entities

People

  • Daniel E. Koditschek
  • Kumpati S. Narendra

Organizations

  • Yale University

Tags

DTIC Thesaurus Topics

  • Classification
  • Coordinate Systems
  • Differential Equations
  • Digital Computers
  • Eigenvalues
  • Eigenvectors
  • Equations
  • Homogeneity
  • Instability
  • Linear Systems
  • Military Research
  • Nonlinear Systems
  • Polynomials
  • Trajectories
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

  • Linear Algebra
  • Theoretical Analysis.