## 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.

**Download:** **PDF**

### Submission history

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

**Unique-IP document downloads:** 15 times

Vixra.org is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary.
In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution.
Vixra.org will not be responsible for any consequences of actions that result from any form of use of any documents on this website.

**Add your own feedback and questions here:**

*You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.*

*
*