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In direct [[tensor]] form that is independent of the choice of coordinate system, these governing equations are:<ref name=Slau>Slaughter, W. S., (2002), ''The linearized theory of elasticity'', Birkhauser.</ref>
* [[Cauchy momentum equation]], which is an expression of [[Newton's laws of motion#Newton's second law|Newton's second law]]. In convective form it is written as: <math display="block">\boldsymbol{\nabla} \cdot \boldsymbol{\sigma} + \mathbf{F} = \rho \ddot{\mathbf{u}} </math>
* [[Infinitesimal strain theory|Strain-displacement]] equations: <math display="block">\boldsymbol{\varepsilon} = \tfrac{1}{2} \left[\boldsymbol{\nabla}\mathbf{u} + (\boldsymbol{\nabla}\mathbf{u})^\mathrm{T}\right]</math>
* [[Constitutive equations]]. For elastic materials, [[Hooke's law]] represents the material behavior and relates the unknown stresses and strains. The general equation for Hooke's law is <math display="block"> \boldsymbol{\sigma} = \mathsf{C}:\boldsymbol{\varepsilon},</math>
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