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Varignon's Theorem (mechanics)
Varignon's theorem is a theorem of French mathematician Pierre Varignon (1654–1722), published in 1687 in his book ''Projet d'une nouvelle mécanique''. The theorem states that the torque of a resultant of two concurrent forces about any point is equal to the algebraic sum of the torques of its components about the same point. In other words, "If many concurrent forces are acting on a body, then the algebraic sum of torques of all the forces about a point in the plane of the forces is equal to the torque of their resultant about the same point." Proof Consider a set of ''N'' force vectors \mathbf_1, \mathbf_2, ..., \mathbf_N that concur at a point \mathbf in space. Their resultant is: :\mathbf=\sum_^N \mathbf_i . The torque of each vector with respect to some other point \mathbf_1 is : \mathbf_^ = (\mathbf-\mathbf_1) \times \mathbf_i . Adding up the torques and pulling out the common factor (\mathbf-\mathbf), one sees that the result may be expressed solely in terms of \ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pierre Varignon
Pierre Varignon (1654 – 23 December 1722) was a French mathematician. He was educated at the Jesuit College and the University of Caen, where he received his M.A. in 1682. He took Holy Orders the following year. Varignon gained his first exposure to mathematics by reading Euclid and then Descartes' ''La Géométrie''. He became professor of mathematics at the Collège Mazarin in Paris in 1688 and was elected to the Académie Royale des Sciences in the same year. In 1704 he held the departmental chair at Collège Mazarin and also became professor of mathematics at the Collège Royal. He was elected to the Berlin Academy in 1713 and to the Royal Society in 1718. Many of his works were published in Paris in 1725, three years after his death. His lectures at Mazarin were published in Elements de mathematique' in 1731. Varignon was a friend of Newton, Leibniz, and the Bernoulli family. Varignon's principal contributions were to graphic statics and mechanics. Except for l'H ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
