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Book Chapter

On the Equations Expressing the Conditions of Equilibrium, or the Laws of Interior Motion, of an Elastic or Nonelastic Solid

By
Augustin-Louis Cauchy
Augustin-Louis Cauchy
1828
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Published:
January 01, 2007

Abstract

In researching equations expressing the conditions of equilibrium or the laws of interior motion of solid or fluid bodies, we can consider these bodies either as continuous masses whose density varies from one point to another by imperceptible degrees or as systems of distinct material points, separated from one another by extremely small distances. It is in the former sense that fluids have been considered in a previous article and in various papers on mechanics published to date. We intend to consider solid bodies in the same sense here as well.

Therefore, let M be the mass of a solid body in equilibrium, m an infinitely small particle or portion taken at random within this mass, x, y, z the coordinates of the particle m on three rectangular axes, and ρ the density of the solid body at the point (x, y, z). If we call p′, p″, p‴ the pressures or tensions exerted at point (x, y, z) and on the side of the positive coordinates, against three planes parallel to the y, z, the z, x, and the x, y planes, the algebraic projections of these forces p′, p″, p‴ on the coordinate axes will be symmetrical [see page 47 of the second volume], and consequently could be represented by the quantities

Furthermore, if, after having passed a plane through point (x, y, z), we draw from this point and onto each of the half-axes perpendicular to the plane two segments —the first being inversely proportional to the

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Contents

Society of Exploration Geophysicists Geophysics Reprint Series

Classics of Elastic Wave Theory

Michael A. Pelissier
Michael A. Pelissier
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Henning Hoeber
Henning Hoeber
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Norbert van de Coevering
Norbert van de Coevering
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Ian F. Jones
Ian F. Jones
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Society of Exploration Geophysicists
Volume
24
ISBN electronic:
9781560801931
Publication date:
January 01, 2007

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