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In case of land vehicles like cars, tanks etc., which use the ENU-system (East-North-Up) as external reference (World frame), the vehicle's (body's) positive y- or pitch axis always points to its left, and the positive z- or yaw axis always points up. World frame's origin is fixed at the center of gravity of the vehicle.
The XYZ system rotates, while xyz is fixed. Starting with XYZ overlapping xyz, a composition of three extrinsic rotations can be used to reach any target orientation for XYZ. The Euler or Tait–Bryan angles (α, β, γ) are the amplitudes of these elemental rotations. For instance, the target orientation can be reached as follows (note the ...
This article uses the standard notation ISO 80000-2, which supersedes ISO 31-11, for spherical coordinates (other sources may reverse the definitions of θ and φ): . The polar angle is denoted by [,]: it is the angle between the z-axis and the radial vector connecting the origin to the point in question.
A point P has coordinates (x, y) with respect to the original system and coordinates (x′, y′) with respect to the new system. [1] In the new coordinate system, the point P will appear to have been rotated in the opposite direction, that is, clockwise through the angle . A rotation of axes in more than two dimensions is defined similarly.
Another common coordinate system for the plane is the polar coordinate system. [7] A point is chosen as the pole and a ray from this point is taken as the polar axis. For a given angle θ, there is a single line through the pole whose angle with the polar axis is θ (measured counterclockwise from the axis to the line).
The particular half-Heusler compounds of interest as thermoelectric materials (space group ) are the semiconducting ternary compounds with a general formula XYZ where X is a more electropositive transition metal (such as Ti or Zr), Y is a less electropositive transition metal (such Ni or Co), and Z is heavy main group element (such as Sn or Sb).
For the affine building, an apartment is a simplicial complex tessellating Euclidean space E n−1 by (n − 1)-dimensional simplices; while for a spherical building it is the finite simplicial complex formed by all (n − 1)! simplices with a given common vertex in the analogous tessellation in E n−2.
Geodetic latitude and geocentric latitude have different definitions. Geodetic latitude is defined as the angle between the equatorial plane and the surface normal at a point on the ellipsoid, whereas geocentric latitude is defined as the angle between the equatorial plane and a radial line connecting the centre of the ellipsoid to a point on the surface (see figure).