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Statements

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dbr:Poloidal–toroidal_decomposition
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Toroidale-Poloidale Zerlegung 极向–环向分解 Poloidal–toroidal decomposition
rdfs:comment
In vector calculus, a topic in pure and applied mathematics, a poloidal–toroidal decomposition is a restricted form of the Helmholtz decomposition. It is often used in the spherical coordinates analysis of solenoidal vector fields, for example, magnetic fields and incompressible fluids. 在向量分析中,极向–环向分解(英文:poloidal–toroidal decomposition)是亥姆霍兹分解的一个受限制的形式,常用于螺线向量场在球坐标系下的分析,如磁场和不可压缩流体等。考虑一个三维向量场F满足 可以被表示为一个轴矢量场(toroidal vector field)和一个极矢量场(poloidal vector field)的和: 其中是球坐标中的径向矢量,纵场为 为一标量场,横场为 为一标量场。这一向量分解法是对称的,因为纵场的旋度是横场,而横场的旋度是纵场。纵场与球心在原点的球面相切 , 而横场的旋度同样地与这些球面相切 . 若标量场和的平均值在任意半径为的球面上都等于零,则这一分解方式是唯一的。 Die Toroidale-Poloidale Zerlegung ist eine Zerlegung eines dreidimensionalen, divergenzfreien Vektorfeldes, z. B. des Erdmagnetfeldes, in zwei Anteile, die jeweils nur von einem eindeutigen Skalarfeld abhängen.
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Die Toroidale-Poloidale Zerlegung ist eine Zerlegung eines dreidimensionalen, divergenzfreien Vektorfeldes, z. B. des Erdmagnetfeldes, in zwei Anteile, die jeweils nur von einem eindeutigen Skalarfeld abhängen. 在向量分析中,极向–环向分解(英文:poloidal–toroidal decomposition)是亥姆霍兹分解的一个受限制的形式,常用于螺线向量场在球坐标系下的分析,如磁场和不可压缩流体等。考虑一个三维向量场F满足 可以被表示为一个轴矢量场(toroidal vector field)和一个极矢量场(poloidal vector field)的和: 其中是球坐标中的径向矢量,纵场为 为一标量场,横场为 为一标量场。这一向量分解法是对称的,因为纵场的旋度是横场,而横场的旋度是纵场。纵场与球心在原点的球面相切 , 而横场的旋度同样地与这些球面相切 . 若标量场和的平均值在任意半径为的球面上都等于零,则这一分解方式是唯一的。 In vector calculus, a topic in pure and applied mathematics, a poloidal–toroidal decomposition is a restricted form of the Helmholtz decomposition. It is often used in the spherical coordinates analysis of solenoidal vector fields, for example, magnetic fields and incompressible fluids.
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