How is dS 2 calculated?
The position vector between two points close together in flat 3D space is simply dr = dxi + dyj + dzk. So the distance between these two points is ds2 = dr. dr = dx2 + dy2 + dz2 which is exactly what we expect from Pythagoros!
What do you mean by Cartesian coordinates?
The Cartesian coordinates (also called rectangular coordinates) of a point are a pair of numbers (in two-dimensions) or a triplet of numbers (in three-dimensions) that specified signed distances from the coordinate axis.
What is phi direction?
More about Phi According to standard convention, phi is traced in anticlockwise direction from the reference +X axis. The normal anticlockwise direction is +X to +Y to -X to -Y then back to +X. And phi is the angle between this vertical half plane and the +X axis.
How do you solve a Cartesian equation?
To obtain a Cartesian equation from parametric equations we must eliminate t. We do this by rearranging one of the equations for x or y, to make t the subject, and then substituting this into the other equation. Hence the Cartesian equation for the parametric equation x = t − 2, y = t2 is y = (x + 2)2.
What do you need to know about a Cartesian coordinate system?
In these cases, we need to find the differential length change (dl), differential area change (ds), and differential volume change (dv) in the chosen coordinate system. Cartesian coordinate system is length based, since dx, dy, dz are all lengths.
What is the differential length change in a Cartesian coordinate system?
In Cartesian coordinate systems, since dx, dy, dz are already length based, h1 = h2 = h3 = 1. From the above discussion, we can see the differential length changes dl1, dl2, dl3 are: where h1, h2, h3 may be functions of u1, u2, and u3.
When is a point located in an orthogonal coordinate system?
If these three surfaces (in fact, their normal vectors) are mutually perpendicular to each other, we call them orthogonal coordinate system. In Cartesian coordinate system, a point is located by the intersection of the following three surfaces: This is shown in the figure below. , , and are the unit vectors in the three coordinate directions.
How is a co-ordinate system related to a geodetic datum?
A National geodetic co-ordinate system is related to its Geodetic Datum, which, in turn, is defined by the following: A defined geodetic reference ellipsoid, in terms of the a,b or a,f parameters. A defined orientation, position and scale of that Geodetic Datum in space.