Chaos Displayed by Solutions of a Forced Pendulum Equation with a Fifth- Order Polynomial for the Damping Terms

Abstract

Solutions of a forced pendulum equation of one degree-of-freedom with nonlinear damping terms have been studied for chaotic and dissipative behavior. This equation can simulate phenomena in which vortex shedding from oscillating and rotating bodies is involved. The characteristic properties of this equation, that is, its singular points, attractors, separatrices, etc. are investigated and related to their physical meaning. A novel attractor is found that represents simultaneously autorotation and self-sustained oscillation. Chaotic behavior is studied with Poincare maps and power spectra. Strange attractors exist which are insensitive to various pendulum coefficients. Of Navy interest are pendulum-type equations that model the rolling motion of ships. This motion can exhibit chaotic behavior. Another example of Navy interest is the usefulness of an extended pendulum equation to describe rotating and oscillating objects in a fluid, a problem whose solution otherwise would require the numerical integration of a set of nonlinear partial differential equations. This case will be studied in this report in more detail. (KR)

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1990
Accession Number
ADA229496

Entities

People

  • Hans J. Lugt
  • Michael L. Brabanski

Tags

Communities of Interest

  • Air Platforms
  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Autorotation
  • Classification
  • Coefficients
  • Differential Equations
  • Equations
  • Flow
  • Fluid Flow
  • Frequency
  • Mathematics
  • Oscillation
  • Partial Differential Equations
  • Pendulums
  • Power Spectra
  • Rotation
  • Spectra
  • Vortex Shedding
  • Vortices

Fields of Study

  • Mathematics

Readers

  • Control Systems Engineering.
  • Wave Propagation and Nonlinear Chaotic Dynamics.