Orthogonal Coordinates

Question

I'm hoping someone could give me a good definition of "orthogonal coordinates." Attempts to find one online has left me only with a vague idea. A reference text would be appreciated.

Answer 1

Orthogonal coordinates are coordinate surface which meet at right angles.

What are coordinate surfaces? There are n dimensions in a coordinate system. A plane in which only one dmension's/coordinate's value is constant is called the coordinate surface. For ex In a 3d coordinate system let x=3 be an equation of plane. This plane is a coordinate surface.

Now if in any coordinate system is such that all coordinate surfaces are perpendicular then this surface is called orthogonal coordinate system. For ex on a plane of paper draw coordinate axes and draw horizontal and vertical lines. Now this is a orthogonal coordinate system. If you keep one end of the page fixed and rotate it from the other end then this also is an orthogonal coordinate system.