基本固体引力多极矩的封闭形式
Closed form expressions for gravitational multipole moments of elementary solids
摘要：
也许推导两个质量之间的牛顿引力相互作用的最有力的方法是多极展开。一旦为特定形状计算了内部多极，该形状就可以旋转，平移，甚至可以用公认的方法转换为外部多极。多极展开的最困难的阶段是产生初始的内部多极矩，而不诉诸于三维数值积分的复杂功能。以前的工作已经产生了表达式的低程度内多极某些基本固体。这项工作更进一步，提出了封闭形式的所有程度和订单的表达式。这些固体的组合，结合上述多极变换，可以用来模拟精密引力实验中经常使用的复杂结构。
英文摘要：
Perhaps the most powerful method for deriving the Newtonian gravitational interaction between two masses is the multipole expansion. Once inner multipoles are calculated for a particular shape this shape can be rotated, translated, and even converted to an outer multipole with well established methods. The most difficult stage of the multipole expansion is generating the initial inner multipole moments without resorting to three dimensional numerical integration of complex functions. Previous work has produced expressions for the low degree inner multipoles for certain elementary solids. This work goes further by presenting closed form expressions for all degrees and orders. A combination of these solids, combined with the aforementioned multipole transformations, can be used to model the complex structures often used in precision gravitation experiments.
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