NONLINEAR OSCILLATIONS IN A SECOND ORDER SYSTEM,

Abstract

Relaxation oscillations are investigated. A number of analytic curves are obtained which serve as upper and lower bounds on solution trajectories in this plane. In many cases, piecewise connection of such bounding curves provide annular regions within which periodic orbits lie. The number, location, stability and amplitude bounds of periodic solutions may be determined in this manner. When the method is applied to the equation of van der Pol, the upper and lower bounds obtained for the amplitude of the unique periodic solutions compare favourably with the known asymptotic expansion of the amplitude. (Author)

Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1964
Accession Number
AD0433472

Entities

People

  • Peter James Ponzo

Organizations

  • University of Illinois Urbana–Champaign

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Amplitude
  • Asymptotic Series
  • Equations
  • Mathematics
  • Oscillation
  • Trajectories

Fields of Study

  • Mathematics

Readers

  • Approximation Theory.
  • Atmospheric Science / Meteorology, specifically Wind Wave Turbulence.
  • Combustion Dynamics and Shock Wave Physics.

Technology Areas

  • Space
  • Space - Orbital Debris