Laplace Equation
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Laplace Equation
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1. The elliptic partial differential equation
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where Missing Image:img src="SP7_l_files/lapeq2.gif" align="bottom" is a scalar
function of position, and Missing Image:img src="SP7_l_files/del.gif" align="bottom"^{2}
is the Laplacian operator. In rectangular Cartesina coordinates
x, y, z , this equation may be written
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The Laplace equation is satisfied, for example, by the
velocity potential in an irrotational flow, by gravitational
potential in free space, by electrostatic potential in the steady
flow of electric currents in solid conductors, and by the steady-state
temperature distribution in solids. A solution of the Laplace
equation is called a harmonic function. Compare Poisson
equation.
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2. An equation for the speed of sound. See Laplacian
speed of sound.
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References
This article is based on NASA's Dictionary of Technical Terms for Aerospace Use