# Ellipsoidal Coordinates ("x" cartesian coordinate)

## Description

Ellipsoidal coordinates are a three-dimensional orthogonal coordinate system that generalizes the two-dimensional elliptic coordinate system. Unlike most three-dimensional orthogonal coordinate systems that feature quadratic coordinate surfaces, the ellipsoidal coordinate system is not produced by rotating or projecting any two-dimensional orthogonal coordinate system.

Related formulas## Variables

x | cartesian coordinate (dimensionless) |

a | semi-principal axis of length a (dimensionless) |

λ | orthogonal coordinate (dimensionless) |

μ | orthogonal coordinate (dimensionless) |

ν | orthogonal coordinate (dimensionless) |

b | semi-principal axis of length b (dimensionless) |

c | semi-principal axis of length c (dimensionless) |