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coordinate system

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The Four Main Coordinate Systemsclick for a larger image
The Four Main Coordinate Systems
coordinate systemclick for a larger image
coordinate system

coordinate system

() A system, resembling that of latitude and longitude on the Earth, by which the direction of a celestial body or a point in the sky can be specified. The direction is defined and determined by two spherical coordinates, referred to a fundamental great circle lying on the celestial sphere and a point on the fundamental circle (see illustration). One coordinate (a) is the angular distance of the celestial body measured perpendicular to the fundamental circle along an auxiliary great circle passing through the body and the poles of the fundamental circle. The other coordinate (b) is the angular distance measured along the fundamental circle from a selected zero point to the intersection of the auxiliary circle.

There are four main coordinate systems: the equatorial, horizontal, ecliptic, and galactic coordinate systems (see table). They are all centered on the Earth. Transformations can be made from one system to another by means of the relationships between the angles and sides of the relevant spherical triangles. The astronomical triangle, for example, relates equatorial and horizontal coordinates; the triangle formed by the celestial body and the poles of the equator and ecliptic relates equatorial and ecliptic coordinates. See also heliocentric coordinate system.

Collins Dictionary of Astronomy © Market House Books Ltd, 2006
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Because the projection of hip joint included angle on coordinate axis relates to multiple factors, in order to simplify analysis, this article only analyses angle variation of hip joint after 3D integration.
Secondly, for each to-be-transformed half [l.sup.[infinity]]-spherical cap in the virtual space, define w to be the coordinate axis that is along the x-axis with the origin displaced at ([+ or -]L/2, 0, 0), respectively.
The most important benefit of such non-parallel reference system is that orientation to the baseline for building site network close to the direction of the site grid axis is in many cases more convenient than using a baseline with direction close to the coordinate axis of the national coordinate system.
By computing the terms of(1) corresponding to each coordinate axis and replacing into the energy equation:
where [[gamma].sub.0] is angle between the positive coordinate axis X and the direction of measurement at initial position of the spindle; [[epsilon].sub.0] is angle between the positive coordinate axis X and the eccentricity [[epsilon].sub.3] of the roundness standard at initial position of the spindle.
here [[gamma].sub.i]--the asymmetry of i-th rectangle of the stair-shape half-period of magnetomotive force in respect of the selected coordinate axis, expressed in electrical degrees of the fundamental space harmonic; v - the number of odd space harmonic; v - the number of even space harmonic.
These campaigns have enabled better and better determinations of the position of the "zeroes" in three dimensions of a rotating Earth centred coordinate axis system.
In order to control the rough position of the workpiece, three Physik Instrumente M-404.2DG linear translation stages are arranged into a coordinate axis frame.
When the coordinate axis is declined to the axis of the circle, the measured circle appears as an ellipse.
where: "[]", "{}", and "x" mean: matrix, vector and vector product; [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is the rotation matrix of the coordinate axis system related to the base (0) coordinate system; [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is the end-effector's position vector related to system (i-1) and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
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