Evaluation of mean values for a forced pendulum with a projection operator method

Kenji Sato, Makoto Okamura

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

Employing a projection operator method, an averaged equation is derived from the equations of motion for a periodically forced pendulum with a damping term. A model equation for the ensemble average is derived from the averaged equation under some assumptions. In addition, the ensemble average is obtained by direct numerical simulation of the pendulum equations. The solutions of the model equation exhibit fair agreement with the numerical solutions for chaotic motion.

Original languageEnglish
Pages (from-to)1-12
Number of pages12
JournalProgress of Theoretical Physics
Volume108
Issue number1
DOIs
Publication statusPublished - Jul 1 2002
Externally publishedYes

Fingerprint

pendulums
projection
operators
evaluation
direct numerical simulation
equations of motion
damping

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy (miscellaneous)

Cite this

Evaluation of mean values for a forced pendulum with a projection operator method. / Sato, Kenji; Okamura, Makoto.

In: Progress of Theoretical Physics, Vol. 108, No. 1, 01.07.2002, p. 1-12.

Research output: Contribution to journalArticle

@article{d0c492431bdc4a0c8ba7d7da6c92ed90,
title = "Evaluation of mean values for a forced pendulum with a projection operator method",
abstract = "Employing a projection operator method, an averaged equation is derived from the equations of motion for a periodically forced pendulum with a damping term. A model equation for the ensemble average is derived from the averaged equation under some assumptions. In addition, the ensemble average is obtained by direct numerical simulation of the pendulum equations. The solutions of the model equation exhibit fair agreement with the numerical solutions for chaotic motion.",
author = "Kenji Sato and Makoto Okamura",
year = "2002",
month = "7",
day = "1",
doi = "10.1143/PTP.108.1",
language = "English",
volume = "108",
pages = "1--12",
journal = "Progress of Theoretical Physics",
issn = "0033-068X",
publisher = "Published for the Research Institute for Fundamental Physics by Physical Society of Japan",
number = "1",

}

TY - JOUR

T1 - Evaluation of mean values for a forced pendulum with a projection operator method

AU - Sato, Kenji

AU - Okamura, Makoto

PY - 2002/7/1

Y1 - 2002/7/1

N2 - Employing a projection operator method, an averaged equation is derived from the equations of motion for a periodically forced pendulum with a damping term. A model equation for the ensemble average is derived from the averaged equation under some assumptions. In addition, the ensemble average is obtained by direct numerical simulation of the pendulum equations. The solutions of the model equation exhibit fair agreement with the numerical solutions for chaotic motion.

AB - Employing a projection operator method, an averaged equation is derived from the equations of motion for a periodically forced pendulum with a damping term. A model equation for the ensemble average is derived from the averaged equation under some assumptions. In addition, the ensemble average is obtained by direct numerical simulation of the pendulum equations. The solutions of the model equation exhibit fair agreement with the numerical solutions for chaotic motion.

UR - http://www.scopus.com/inward/record.url?scp=0036653999&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0036653999&partnerID=8YFLogxK

U2 - 10.1143/PTP.108.1

DO - 10.1143/PTP.108.1

M3 - Article

AN - SCOPUS:0036653999

VL - 108

SP - 1

EP - 12

JO - Progress of Theoretical Physics

JF - Progress of Theoretical Physics

SN - 0033-068X

IS - 1

ER -