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

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.

Cite this paper

G. Zhou, "A Geometrical Theorem about the Static Equilibrium of a Common-point-force System and its Application,"*Open Journal of Applied Sciences*, Vol. 3 No. 1, 2013, pp. 65-69. doi: 10.4236/ojapps.2013.31B1013.

G. Zhou, "A Geometrical Theorem about the Static Equilibrium of a Common-point-force System and its Application,"

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[1] H. William, T. S. H. George, J. Ping and C. W. L. Henry, “A Hybrid Genetic Algorithm for the Multi-depot Vehicle Routing Problem,” Engineering Applications of Artificial intelligence, Vol. 21, No. 4, 2008, pp. 548-557. doi:10.1016/j.engappai.2007.06.001

[2] Benoit Crevier, Jean-François Cordeau and Gilbert Laporte, “The Multi-depot Vehicle Routing Problem with Inter-depot Routes,” European Journal of Operational Research, Vol. 176, No. 4, 2007, pp. 756-773. doi:10.1016/j.ejor.2005.08.015

[3] Rubén Ruiz, Concepción Maroto and Javier Alcaraz, “A Decision Support System for a Real Vehicle Routing Problem,” European Journal of Opera-tional Research, Vol. 153, No. 3, 2004, pp. 593-606. doi:10.1016/S0377-2217(03)00265-0

[4] Bruce L.Golden, Gilbert Laporte and éric D. Taillard, “An Adaptive Memory Heuristic for a Class of Vehicle Routing Problems with Minmax Objective,” Computers & Operations Research, Vol. 24, No. 5, 1997, pp. 445-452. doi:10.1016/S0305-0548(96)00065-2

[5] Emmanouil E. Zachariadis, Christos D. Tarantilis and Chris T. Kiranoudis, “An Adaptive Memory Methodology for the Vehicle Routing Problem with Simultaneous Pick-ups and Deliveries,” European Journal of Operational Research, Vol. 202, No. 2, 2002, pp. 401-411. doi:10.1016/j.ejor.2009.05.015

[6] C. D. Collinson, “Introductory Mechanics,” London: Edward Arnold Ltd., Vol. 2-3, 1980, pp. 41-42.

[7] Z. X. Zhu and Q. Z. Zhou, “Theoretical Mechanics,” Beijing: Beijing University Press, Vol. 292-293, 1982, pp. 313-314.

[8] G. Y. Yu and G. Q. Zhou, “Electrodynamics,” Beijing: Higher Education Press, Vol. 8-9, 1997, pp. 51-52.

[9] K. David, C. Field and Wave, “Electromagnetics,” New York: Addison-Wesley Publishing Company, Inc., 1983. pp. 84-85.