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equation of motion

Augustin Louis Cauchy (August 21, 1789 – May 23, 1857)

Augustin Louis Cauchy ( 21 August 1789 - 23 May 1857) was a French mathematician and mechanician. In mechanics, he in 1822 formalized the stress concept in the context of three-dimensional thoery, showed its properties as consisting of a 3 by 3 symmetric arrays of numbers that transform as a tensor, derived the equations of motion for a continuum in terms of the components of stress, and gave the specific development of the theory of linear elasticity for isotropic solids. As part of his work, Cauchy also introduced the equations which express the six components of strain, three extensinal and three shear, in terms of derivatives of displacements for the case when all those derivatives are much smaller than unity; similar expressions had been given earlier by Euler in expressing rates of straining in terms of the derivatives of the velocity field in a fluid. (cited from Mechanics of Solids by J.R. Rice) Read more...

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