“spherical polar coordinates”的概念、定义、翻译、参考文献-科学参考

spherical polar coordinates

Physics

See polar coordinates.

Mathematics

Suppose that three mutually perpendicular directed lines Ox, Oy, and Oz, intersecting at the point O, and forming a right-handed system are taken as coordinate axes. For any point P, let M be the projection of P on the xy-plane. Let r = |OP|, let θ‎ be the angle ∠zOP in radians (0 ≤ θ‎ ≤ π‎) and let ϕ‎ be the angle ∠xOM in radians (0 ≤ ϕ‎ < 2π‎). Then (r, θ‎, π‎) are the spherical polar coordinates of P. (The point O gives no value for θ‎ or ϕ‎, but is simply said to correspond to r = 0.) The Cartesian coordinates (x,y,z) of P in terms of r, θ‎, and ϕ‎ are given by

$x = r sin θ cos ϕ, y = r sin θ sin ϕ, z = r cos θ .$

Compare cylindrical polar coordinates.

Statistics

Coordinates that specify the location of a point in three dimensions. The basis of these coordinates is a set of three mutually perpendicular axes, Ox, Oy, and Oz, that intersect at O. Consider a point P, in three-dimensional space, at a distance r from O, the angle being equal to θ. Let OM be the projection of OP on the xy-plane and let the angle be equal to ϕ. The spherical polar coordinates of P are (r, θ, ϕ), where 0° ≤ θ ≤ 180°, 0° ≤ ϕ < 360°. These coordinates are related to the alternative Cartesian coordinates (x, y, z) by $spherical polar coordinates$
Spherical polar coordinates. Using Cartesian coordinates, the point P would be represented by (x, y, z), with x=r sin θ cos ϕ, y= r sin θ sin ϕ, z=r cos θ.

Electronics and Electrical Engineering

A technique for giving three-dimensional coordinates of a point based on its distance from a fixed origin and two angles relative to two perpendicular axes through that origin. The radial distance coordinate r can be interpreted as a move up the vertical z-axis, which is then followed by a rotation by polar angle θ down towards the horizontal x-axis, and finally a rotation by the azimuth angle φ about the z-axis towards the y-axis. There is no fixed convention as to the Greek symbols used for the two angles, so care is needed when using them. See also cylindrical polar coordinates; polar coordinates.
Spherical polar coordinates

单词	spherical polar coordinates
释义	spherical polar coordinates Physics See polar coordinates. Mathematics Suppose that three mutually perpendicular directed lines Ox, Oy, and Oz, intersecting at the point O, and forming a right-handed system are taken as coordinate axes. For any point P, let M be the projection of P on the xy-plane. Let r = \|OP\|, let θ‎ be the angle ∠zOP in radians (0 ≤ θ‎ ≤ π‎) and let ϕ‎ be the angle ∠xOM in radians (0 ≤ ϕ‎ < 2π‎). Then (r, θ‎, π‎) are the spherical polar coordinates of P. (The point O gives no value for θ‎ or ϕ‎, but is simply said to correspond to r = 0.) The Cartesian coordinates (x,y,z) of P in terms of r, θ‎, and ϕ‎ are given by $x = r sin θ cos ϕ, y = r sin θ sin ϕ, z = r cos θ .$ Compare cylindrical polar coordinates. Statistics Coordinates that specify the location of a point in three dimensions. The basis of these coordinates is a set of three mutually perpendicular axes, Ox, Oy, and Oz, that intersect at O. Consider a point P, in three-dimensional space, at a distance r from O, the angle being equal to θ. Let OM be the projection of OP on the xy-plane and let the angle be equal to ϕ. The spherical polar coordinates of P are (r, θ, ϕ), where 0° ≤ θ ≤ 180°, 0° ≤ ϕ < 360°. These coordinates are related to the alternative Cartesian coordinates (x, y, z) by $spherical polar coordinates$ Spherical polar coordinates. Using Cartesian coordinates, the point P would be represented by (x, y, z), with x=r sin θ cos ϕ, y= r sin θ sin ϕ, z=r cos θ. Electronics and Electrical Engineering A technique for giving three-dimensional coordinates of a point based on its distance from a fixed origin and two angles relative to two perpendicular axes through that origin. The radial distance coordinate r can be interpreted as a move up the vertical z-axis, which is then followed by a rotation by polar angle θ down towards the horizontal x-axis, and finally a rotation by the azimuth angle φ about the z-axis towards the y-axis. There is no fixed convention as to the Greek symbols used for the two angles, so care is needed when using them. See also cylindrical polar coordinates; polar coordinates. Spherical polar coordinates
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