# Demos-1

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Elliptic and Cartesian coordinates

## Elliptic and Cartesian coordinates

Almost all tasks, involving Mathieu functions have elliptical geometry.

Let us assume an ellipse in the (x, y) plane whose equation is (1)

 (1)

where a > b are major and minor semi-axes of ellipse. The semi-focal distance f is given by (2)

 (2)

Conversion between Cartesian and elliptic coordinates are given by equation (3) [1]

 (3)

from which one can obtain the forward and backward conversion formulas:

Conversion from elliptic to Cartesian coordinates Conversion from Cartesian to elliptic coordinates
(function mathieu_ell2cart) (function mathieu_cart2ell)

For better understanding of elliptical coordinates you can use the demo named "Elliptic and Cartesian coordinates" we have an ellipse with semi-axes a = 5, b = 4 and semi-focal f = 3.

This demo uses `mathieu_ell2cart` function.

You can launch it from Scilab menu "? -> Scilab Demonstrations -> Mathieu functions -> Elliptic and Cartesian coordinates".

### Bibliography

1. N. W. McLachlan, Theory and Application of Mathieu Functions, Oxford Univ. Press, 1947.

Created: 6 years 7 months ago

Updated: 2 years 3 months ago

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