A Geometrical Theorem about the Static Equilibrium of a Common-point-force System and its Application

Guo-quan Zhou

Department of Physics, Wuhan University, Wuhan, Hubei, China.

DOI: 10.4236/ojapps.2013.31B1013                

Abstract

A geometrical theorem for the static equilibrium of a common-point-force system has been proven by means of virtual-work principle: The equilibrium point of a common-point force system has a minimal weighted distance summation to every fixed point arbitrarily given on each force line with a weighing factor proportional to corresponding force value. Especially the mechanical simulating technique for its inverse problem has been realized by means of pulley block. The conclusions for the inverse problem derived from mechanic method are in accordance with that given by the pure mathematical method, and the self-consistence of the theorem and its inverse problem has been demonstrated. Some application examples in engineering, economy and mathematics have been discussed, especially the possible application in the research of molecular structure, has also been predicted.

Keywords

Spatial Common-point-force System; Static Equilibrium; Minimum Theorem；Principle of Virtual Work; Depot Problem; Transportation

Conflicts of Interest

The authors declare no conflicts of interest.

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