Advertisement

Phase-Plane Portraits

  • Richard H. Enns
  • George C. McGuire
Part of the Undergraduate Texts in Contemporary Physics book series (UTCP)

Abstract

Consider a dynamical system of two coupled ordinary differential equations (ODEs) of the general structure
$$ \dot{x} \equiv \frac{{dx}}{{dt}} = P(x,y),\dot{y} \equiv \frac{{dy}}{{dt}} = Q(x,y) $$
(5.1)
where P and Q are known functions of the dependent variables x and y and the independent variable has been taken to be the time t. In some model equations, the independent variable could be a spatial variable. For compactness, time derivatives will often be indicated in our text discussion by using the dot notation, one dot placed above the dependent variable (e.g., ) indicating a first time derivative, two dots a second time derivative, etc. Similarly, derivatives with respect to a spatial variable will often be indicated by superscripted primes.

Keywords

Singular Point Stationary Point Vortex Point Tangent Field Simple Harmonic Oscillator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • Richard H. Enns
    • 1
  • George C. McGuire
    • 2
  1. 1.Department of PhysicsSimon Fraser UniversityBurnabyCanada
  2. 2.Department of PhysicsUniversity College of the Fraser ValleyAbbotsfordCanada

Personalised recommendations