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 OJAppS  Vol.3 No.1 B1 , April 2013
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.
References

[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.

 
 
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