Definition:Orthogonal Curvilinear Coordinates/Definition 2

Definition
Let $\KK$ be a curvilinear coordinate system in $3$-space.

Let $\QQ_1$, $\QQ_2$ and $\QQ_3$ denote the one-parameter families that define the curvilinear coordinates.

Let $\tuple {q_1, q_2, q_3}$ denote a set of curvilinear coordinates. Let $\KK$ have the property that for every arbitrary pair of coordinate surfaces $q_i \in \QQ_i$ and $q_j \in \QQ_j$ where $i \ne j$:


 * $q_i$ and $q_j$ are orthogonal.

Then $\KK$ is an orthogonal curvilinear coordinate system.

Also see

 * Equivalence of Definitions of Orthogonal Curvilinear Coordinates