## A Solution of the Laplacian Using Geodetic Coordinates

**Authors:** Abdelmajid Ben Hadj Salem

Using the geodetic coordinates $(\varphi,\lambda,h)$, we give the expression of the laplacian $\Delta V=\ds \frac{\partial^2 V}{\partial x ^2}+\frac{\partial^2 V}{\partial y ^2}+\frac{\partial^2 V}{\partial z ^2}$ in these coordinates. A solution of $\Delta V=0$ of type $V=f(\lambda).g(\varphi,h)$ is given. The partial differential equation satisfied by $g(\varphi,h)$ is transformed in an ordinary differential equation of a new variable $u=u(\varphi,h)$.

**Comments:** 7 Pages.

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### Submission history

[v1] 2019-05-26 13:08:57

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