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  "body": "\n## Summary\n\nThe Lamé equations, also called the Navier–Cauchy equations, govern small deformations of a homogeneous isotropic elastic solid.\nTheir unknown is the displacement field $u$, which tells how far each point of the body moves.\nThe material enters through two constants, the Lamé parameters $\\lambda$ and $\\mu$.\nIn the static case they form an elliptic system, and the time-dependent version predicts two kinds of elastic waves, pressure waves and shear waves.\n\n## Explanations\n\n### L1 human\n\nPress on a rubber block and every point inside it moves a little.\nThe Lamé equations say how these small displacements balance the internal stresses and the outside forces.\nThe parameter $\\mu$ measures resistance to shearing and $\\lambda$ adds resistance to change of volume.\nA displacement that just moves or turns the whole body without bending it costs no stress and solves the equations with no force.\nEarthquake waves are solutions of the time-dependent equations: the faster pressure waves arrive first and the shear waves after them.\n",
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