A STUDY OF NONLINEAR OSCILLATORY SYSTEMS WITH MANY DEGREES OF FREEDOM IN THE PRESENCE OF RANDOM PERTURBATIONS (ISSLEDOVANIE NELINEINYKH KOLEBATELNYKH SISTEM SO MNOGIMI STEPENYAMI SVOBODY PRI NALICHII SLUCHAINYKH VOZMUSHCHENII),

Abstract

Real systems are always subject to the mutual action of systematic and random perturbations. Actually, purely harmonic oscillations do not exist. Oscillations are actually modulations; their amplitude and phase change slowly in time. The problem of investigating the mutual action of random forces on nonlinear oscillatory systems is realized by reducing the real random process to a process without a time lag and without using the Fokker, Plank and Kolmogorov equations. In the article, the behavior of the amplitude and phase of an equivalent oscillatory system is examined in the case when the system is under the action of stationary random perturbations, upon which a change of amplitude and phase is presented as the Markov process. The result is the statistic description of an oscillatory system under single-frequency conditions. (Author)

Document Details

Document Type
Technical Report
Publication Date
Sep 22, 1967
Accession Number
AD0675236

Entities

People

  • V. G. Kolomiets

Organizations

  • National Air and Space Intelligence Center

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Amplitude
  • Equations
  • Frequency
  • Kolmogorov Equations
  • Markov Processes
  • Mathematics
  • Modulation
  • Oscillation
  • Perturbations
  • Stationary

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Control Systems Engineering.
  • Information Retrieval