Four expressions involving sums of position and velocity coordinates bounding the total angular momentum of particle systems, and by extension of any continuous or discontinuous material systems, are derived which are tighter for any particle configuration than similar inequalities derived by Sundman (Acta Math 36:105, 1913), Saari (Conference board of the mathematical sciences, No. 104, 2005. http://books.google.ch/books?id=uNXgf2X1GeYC) and Scheeres (Celest Mech Dyn Astron 113:291–320, 2012. https://doi.org/10.1007/s10569-012-9416-0). Eight distinct inequalities can thus be ordered according to their tightness to angular momentum.

中文翻译：

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粒子系统中的角动量界限

四个表达式涉及位置和速度坐标的总和限制粒子系统的总角动量，并通过扩展任何连续或不连续的材料系统，推导出对于任何粒子配置比由 Sundman 导出的类似不等式更紧密（Acta Math 36:105 , 1913)、Saari（数学科学会议委员会，第 104 期，2005 年。http://books.google.ch/books?id=uNXgf2X1GeYC）和 Scheeres（Celest Mech Dyn Astron 113：291-320，2012 年。 https://doi.org/10.1007/s10569-012-9416-0）。因此可以根据它们对角动量的紧密程度对八个不同的不等式进行排序。