Orthogonal coordinates - Wikipedia
In mathematics, orthogonal coordinates are defined as a set of d coordinates = (,, …,) in which the coordinate hypersurfaces all meet at right angles (note that superscripts are indices, not exponents).
19.4: Appendix - Orthogonal Coordinate Systems - Physics …
2021年3月14日 — Cartesian coordinates (rectangular) provide the simplest orthogonal rectangular coordinate system. The unit vectors specifying the direction along the three orthogonal axes are taken to be \((\mathbf{\hat{i}},\mathbf{\hat{j}}, \mathbf{\hat{k}})\).
Orthogonal Coordinate System -- from Wolfram MathWorld
2024年11月26日 — An orthogonal coordinate system is a system of curvilinear coordinates in which each family of surfaces intersects the others at right angles. Orthogonal coordinates therefore satisfy the additional constraint that u_i^^·u_j^^=delta_(ij), (1) where delta_(ij) is the Kronecker delta.
The vector C is orthogonal to both A and B, i.e. it is orthogonal to the plane defined by A and B. The direction of C is determined by the right-hand rule as shown.
Cartesian coordinate system - Wikipedia
A Cartesian coordinate system in two dimensions (also called a rectangular coordinate system or an orthogonal coordinate system [8]) is defined by an ordered pair of perpendicular lines (axes), a single unit of length for both axes, and an orientation for each axis. The point where the axes meet is taken as the origin for both, thus turning ...
We see that the coordinate values zr,,, and ρ θ are all variables of a right triangle! We can use our knowledge of trigonometry to relate them to each other. In fact, we can completely derive the relationship between all six independent coordinate values by considering just two very important right triangles! Æ Hint: Memorize these 2
There are a total of thirteen orthogonal coordinate systems in which Laplace’s equation is separable, and knowledge of their existence (see Morse and Feshbackl) can be useful for solving problems in potential theory.
Orthogonal Coordinate System - an overview - ScienceDirect
The term “orthogonal” (Greek o͗ρθóς, straight, and γωνι´α, angle) refers to the fact of two quantities being perpendicular to each other and therefore independent, as with an orthogonal coordinate system where the axes represent independent directions in space.
Accordingly, many special coordinate systems have been devised to solve problems in particular geometries. The most useful of these systems are orthogonal; that is, at any point in space the vectors aligned with the three coordinate directions are mutually perpendicular.
Orthogonal system - Encyclopedia of Mathematics
2022年3月4日 — An orthogonal coordinate system is a coordinate system in which the coordinate lines (or surfaces) intersect at right angles. Orthogonal coordinate systems exist in any Euclidean space, but, generally speaking, do not exist in an arbitrary space.