coordinatesmathematics
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configuration space
( in mechanics: Configuration space )
The position of a single particle is specified by giving its three coordinates, x, y, and z. To specify the positions of two particles, six coordinates are needed, x1, y1, z1, x2, y2, z2. If there are N particles, 3N coordinates will be needed. Imagine a system...
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physical reference frames
( in reference frame )
The reference frames used in dynamics are known as coordinate systems with axes (lines) emanating from a point known as the origin. The position of a point moving parallel to a plane (plane motion) can be described by two numbers: (1) either the distances of the point from two lines at right angles to one another on the plane (rectangular coordinates), or (2) the length of a line with one end...
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transformation
( in trigonometry: Transformation of coordinates )
A transformation of coordinates in a plane is a change from one coordinate system to another. Thus, a point in the plane will have two sets of coordinates giving its position with respect to the two coordinate systems used, and a transformation will express the relationship between the coordinate systems. For example, the transformation between polar and Cartesian coordinates discussed in the...
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system of locating points in a plane with reference to a fixed point (origin) and an axis through that point. The coordinates are written (r,θ), in which r is the distance from the origin to any desired point and θ is the angle made by the vector r and the axis. A simple relationship exists between Cartesian coordinates given in terms of two reference axes (x,y) and the polar coordinates (r,θ), namely: x = r cos θ, and y = r sin θ.
Polar coordinates, like Cartesian coordinates, may also be used to locate points in three-dimensional space. The system used involves again the radius vector r, which gives distance from the origin, the angle θ, measured between r and the z axis, and a second angle ϕ, measured between the x axis and the projection of r in the x,y plane. This system is essentially identical to that of spherical coordinates; points on Earth, for example, are located in terms of latitude and longitude, which express angles measured with respect to the axis of the Earth’s rotation and with respect to an arbitrary reference of longitude (the Greenwich meridian).
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electromagnetic representation geomagnetic field
...system the vector is decomposed into three components corresponding to the projections of the vector on three mutually orthogonal axes that are usually labeled x, y, z. In polar coordinates the vector is typically described by the length of the vector in the x-y plane, its azimuth angle in this plane relative to the x axis, and a third Cartesian...
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graph mapping graph
In certain cases, polar coordinates (q.v.) provide a more appropriate graphic system, whereby a series of concentric circles with straight lines through their common centre, or origin, serves to locate points on a circular plane. Both Cartesian and polar coordinates...
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configuration space mechanics
The position of a single particle is specified by giving its three coordinates, x, y, and z. To specify the positions of two particles, six coordinates are needed, x1, y1, z1, x2, y2, z2. If there are N particles, 3N coordinates will be needed. Imagine a system...
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physical reference frames reference frame
The reference frames used in dynamics are known as coordinate systems with axes (lines) emanating from a point known as the origin. The position of a point moving parallel to a plane (plane motion) can be described by two numbers: (1) either the distances of the point from two lines at right angles to one another on the plane (rectangular coordinates), or (2) the length of a line with one end...
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transformation trigonometry
A transformation of coordinates in a plane is a change from one coordinate system to another. Thus, a point in the plane will have two sets of coordinates giving its position with respect to the two coordinate systems used, and a transformation will express the relationship between the coordinate systems. For example, the transformation between polar and Cartesian coordinates discussed in the...
Student Encyclopædia Britannica articles specifically written for elementary and high school students.
- Polar, Wind and Geotail at NASA -...
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stellar positions star
Accurate observations of stellar positions are essential to many problems of astronomy. Positions of the brighter stars can be measured very accurately in the equatorial system (the coordinates of which are called right ascension [α, or RA] and declination [δ, or DEC] and are given for some epoch—for example, 1950.0 or, currently, 2000.0). Fainter stars are measured by using...
Student Encyclopædia Britannica articles specifically written for elementary and high school students.
- National Radio Astronomy Observatory - Earth Rotation and Equatorial Coordinates
Student Encyclopædia Britannica articles specifically written for elementary and high school students.
- Polar, Wind and Geotail at NASA - Coordinates
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main reference altitude and azimuth
in astronomy, gunnery, navigation, and other fields, two coordinates describing the position of an object above the Earth. Altitude in this sense is expressed as angular elevation (up to 90°) above the horizon. Azimuth is the number of degrees clockwise from due north (usually) to the object’s vertical circle (i.e., a great circle through the object and the zenith).
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use in military fire control artillery
...sight, which could be revolved in any direction and which was graduated in degrees relative to the axis of the gun bore. The gun’s position and that of the target were marked on a map, and the azimuth (the number of degrees clockwise from due north) between the two was measured. A prominent local feature, or a marker placed some distance from the gun, was then selected as an aiming point,...
Student Encyclopædia Britannica articles specifically written for elementary and high school students.
- Polar, Wind and Geotail at NASA - Coordinates
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