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A group-theoretic approach to the study of small oscillations of a dynamical system with a known symmetry

Technical Report:

Abstract

By way of illustrating how group representations can be gainfully utilized in the study of oscillations of dynamical/mechanical systems with known symmetries, we study the oscillations of a simple dynamical system consisting of three identical masses with a triangular symmetry. The particles are connected by light strings having the same stiffness constant. By use of irreducible representations of the symmetry group of the dynamical system, one obtains the frequencies of the normal modes of oscillation of the system without having to solve the characteristic equation of degree six in the eigenvalue of they system. This approach greatly simplifies the determination of the motion of the system and can easily be extended to other dynamical/mechanical problems with known symmetries. (author). 9 refs, 3 figs, 5 tabs.
Authors:
Publication Date:
Sep 01, 1992
Product Type:
Technical Report
Report Number:
IC-92/304
Reference Number:
SCA: 661100; 661300; PA: AIX-24:008089; SN: 93000932830
Resource Relation:
Other Information: PBD: Sep 1992
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; QUANTUM MECHANICS; GROUP THEORY; EIGENFREQUENCY; IRREDUCIBLE REPRESENTATIONS; OSCILLATION MODES; SYMMETRY GROUPS; 661100; 661300; CLASSICAL AND QUANTUM MECHANICS; OTHER ASPECTS OF PHYSICAL SCIENCE
OSTI ID:
10119396
Research Organizations:
International Centre for Theoretical Physics (ICTP), Trieste (Italy)
Country of Origin:
IAEA
Language:
English
Other Identifying Numbers:
Other: ON: DE93612971; TRN: XA9233091008089
Availability:
OSTI; NTIS (US Sales Only); INIS
Submitting Site:
INIS
Size:
[17] p.
Announcement Date:
Jun 30, 2005

Technical Report:

Citation Formats

Chukwumah, G C. A group-theoretic approach to the study of small oscillations of a dynamical system with a known symmetry. IAEA: N. p., 1992. Web.
Chukwumah, G C. A group-theoretic approach to the study of small oscillations of a dynamical system with a known symmetry. IAEA.
Chukwumah, G C. 1992. "A group-theoretic approach to the study of small oscillations of a dynamical system with a known symmetry." IAEA.
@misc{etde_10119396,
title = {A group-theoretic approach to the study of small oscillations of a dynamical system with a known symmetry}
author = {Chukwumah, G C}
abstractNote = {By way of illustrating how group representations can be gainfully utilized in the study of oscillations of dynamical/mechanical systems with known symmetries, we study the oscillations of a simple dynamical system consisting of three identical masses with a triangular symmetry. The particles are connected by light strings having the same stiffness constant. By use of irreducible representations of the symmetry group of the dynamical system, one obtains the frequencies of the normal modes of oscillation of the system without having to solve the characteristic equation of degree six in the eigenvalue of they system. This approach greatly simplifies the determination of the motion of the system and can easily be extended to other dynamical/mechanical problems with known symmetries. (author). 9 refs, 3 figs, 5 tabs.}
place = {IAEA}
year = {1992}
month = {Sep}
}