Duality in Mechanics

 

作者: P. Le Corbeiller,   Ying‐Wa Yeung,  

 

期刊: The Journal of the Acoustical Society of America  (AIP Available online 1952)
卷期: Volume 24, issue 6  

页码: 643-648

 

ISSN:0001-4966

 

年代: 1952

 

DOI:10.1121/1.1906947

 

出版商: Acoustical Society of America

 

数据来源: AIP

 

摘要:

Given an electric networkEvwhich hasMmeshes andPnode‐pairs, its electric dualEiwill havePmeshes andMnode‐pairs and its classical mechanical analogMfwill haveM+1 nodes,Mindependent node‐pairs, andPindependent node cycles. A second mechanical systemMv, the classical analog ofEi, will haveMcycles andPnode‐pairs. If, for example,M= 2,P= 3, the systemsEvandMv, analogs in the Firestone or “mobility” method, will be governed by two mesh equations, expressing that the algebraic sum of the voltages or velocities around any loop is zero; the systemsEiandMf, also Firestone analogs, will satisfy two node equations, expressing that the algebraic sum of the currents or forces leaving any node is zero. These four sets of equations are identical, interchanging symbols suitably. The consideration of the four systems,Ev,Ei,Mv,Mf, forming a complete set, shows the advantages of the Firestone over the classical system of analogies and suggests a systematic use of duality in mechanical as well as in electrical systems.

 

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