ASYMPTOTIC REPRESENTATION OF THE CYCLE OF VAN DER POL'S EQUATION FOR SMALL DAMPING COEFFICIENTS,

Abstract

The limit cycle of Van der Pol's equation is expanded as a power series of the damping coefficient epsilon, the coefficients being finite trigonometric sums with the time as argument. Because the development was implemented in a fully automatic way on a computer, it has been pushed to a high power of epsilon. Hence, for epsilon as large as 0.75, the estimates given by the series for the amplitude and the period agree to 15 decimal places with their correct values computed on integrating by recurrent power series Van der Pol's equation and its associated variational equation. When epsilon reaches 1.75, the agreement is still within 0.001. (Author)

Document Details

Document Type
Technical Report
Publication Date
Feb 01, 1967
Accession Number
AD0649562

Entities

People

  • A. R. M. Rom
  • Andre Deprit

Organizations

  • Boeing

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Agreements
  • Amplitude
  • Automatic
  • Coefficients
  • Computers
  • Differential Equations
  • Equations
  • Mathematical Analysis
  • Mathematics
  • Power Series
  • Real Variables
  • Variational Equations

Readers

  • Analytical Mechanics
  • Control Systems Engineering.
  • Structural Dynamics.