RESONANCE IN ALMOST LINEAR SYSTEMS.

Abstract

Estimates, useful for all times, are sought for the resonant response of a system with small non-linearity. It is shown that the method of multiple scales can be used to generate a representation which is formally asymptotic at all times and over a significant time interval is a valid approximation to some solution of the system. It is shown, by example that this estimate is not always a useful representation of any one solution for all time. Plausible arguments are given that the approximation is nevertheless useful for the determination of the behavior of a physical system if not of the pathological solutions of the differential equations which may represent it. (Author)

Document Details

Document Type
Technical Report
Publication Date
Aug 01, 1967
Accession Number
AD0662739

Entities

People

  • H. C. Levey
  • J. J. Mahony

Organizations

  • University of Wisconsin–Madison

Tags

DTIC Thesaurus Topics

  • Differential Equations
  • Equations
  • Intervals
  • Linear Systems
  • Linearity
  • Mathematics
  • Resonance
  • Time Intervals

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Quantum spin resonance or Electron Paramagnetic Resonance spectroscopy.
  • Theoretical Analysis.