Definition:Orthogonal Curvilinear Coordinates/Definition 2
Jump to navigation
Jump to search
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
- Results about orthogonal curvilinear coordinates can be found here.
Sources
There are no source works cited for this page. Source citations are highly desirable, and mandatory for all definition pages. Definition pages whose content is wholly or partly unsourced are in danger of having such content deleted. To discuss this page in more detail, feel free to use the talk page. |