“spherical polar coordinates”的概念、定义、习题解题方法及翻译-数学辞典

单词

spherical polar coordinates

释义

spherical polar coordinates

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

Compare cylindrical polar coordinates.

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