Laplace Equation

From ExoDictionary
Jump to: navigation, search
This definition page has been automatically generated.
You can help ExoDictionary by expanding, updating, or correcting it.

This autostub has not yet had its initial copyediting proof and may contain significant formatting and even factual errors. You can improve Exodictionary by cleaning up the page markup and verifying that the definition is correct and then removing this tag.

This autostub has not yet had its initial categorization proof and may be categorized incorrectly. You can improve Exodictionary by removing inappropriate categories and then removing this tag.

Laplace Equation

1. The elliptic partial differential equation

Missing Image:img src="SP7_l_files/lapeq1.gif" align="bottom"

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

Missing Image:img src="SP7_l_files/lapeq3.gif" align="bottom"

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. </dd>
2. An equation for the speed of sound. See Laplacian speed of sound. </dd>


This article is based on NASA's Dictionary of Technical Terms for Aerospace Use