TITLE:
A Geometrical Theorem about the Static Equilibrium of a Common-point-force System and its Application
AUTHORS:
Guo-quan Zhou
KEYWORDS:
Spatial Common-point-force System; Static Equilibrium; Minimum Theorem；Principle of Virtual Work; Depot Problem; Transportation
JOURNAL NAME:
Open Journal of Applied Sciences,
Vol.3 No.1B1,
July
11,
2013
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.