A Study of Damping in Nonlinear Oscillations

Abstract

An investigation is made of nonlinear oscillations in which the damping and static moments are represented by arbitrary polynomial functions of the dependent variable. When the nonlinear damping is small but the static nonlinearities arbitrarily large, an approximate solution is established which leads to expressions for the damping decrement involving elliptic integrals and gamma functions in special cases. An 'effective linear damping' is defined and a generalized formula for this parameter is obtained that is valid for a wide range of nonlinearities in both the damping and static moments. This formula is useful, for instance, in deducing the dynamic-stability parameters of missiles observed in nearly planar motion in free flight.

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Document Details

Document Type
Technical Report
Publication Date
Oct 01, 1966
Accession Number
ADA395527

Entities

People

  • Donn B. Kirk
  • Maurice L. Rasmussen

Organizations

  • Stanford University

Tags

Communities of Interest

  • Air Platforms
  • Materials and Manufacturing Processes
  • Weapons Technologies

DTIC Thesaurus Topics

  • Aerodynamic Configurations
  • Amplitude
  • Coefficients
  • Differential Equations
  • Equations
  • Free Flight
  • Frequency
  • Integral Equations
  • Integrals
  • Lepidoptera
  • Linear Systems
  • Molecular Orbital Theory
  • Nonlinear Differential Equations
  • Numerical Integration
  • Oscillation
  • Oscillators
  • Simultaneous Equations

Fields of Study

  • Engineering
  • Physics

Readers

  • Control Systems Engineering.
  • Electromagnetic Wave Scattering and Antenna Radiation Engineering