论文标题
三体惯性张量
Three-Body Inertia Tensor
论文作者
论文摘要
我们得出了三体系统的惯性张量的一般公式。通过使用三个独立的拉格朗日不确定的乘数来表达与顶点的位置向量相对应的向量，我们介绍了不同质量三个粒子的惯性张量的一般协变表达。 If $m_a/a=m_b/b=m_c/c=ρ$, then the center of mass coincides with the incenter of the triangle and the moment of inertia about the normal axis passing the center of mass is $I=ρabc$, where $m_a$, $m_b$, and $m_c$ are the masses of the particles at $A$, $B$, and $C$, respectively, and $a$, $ b $，和$ c $是行段$ \ overline {bc} $，$ \ overline {ca} $和$ \ overline {ab} $的长度。派生和相应的结果与著名的三角形区域的苍鹭公式密切相关。
We derive a general formula for the inertia tensor of a three-body system. By employing three independent Lagrange undetermined multipliers to express the vectors corresponding to the sides in terms of the position vectors of the vertices, we present the general covariant expression for the inertia tensor of the three particles of different masses. If $m_a/a=m_b/b=m_c/c=ρ$, then the center of mass coincides with the incenter of the triangle and the moment of inertia about the normal axis passing the center of mass is $I=ρabc$, where $m_a$, $m_b$, and $m_c$ are the masses of the particles at $A$, $B$, and $C$, respectively, and $a$, $b$, and $c$ are the lengths of the line segments $\overline{BC}$, $\overline{CA}$, and $\overline{AB}$, respectively. The derivation and the corresponding results are closely related to the famous Heron's formula for the area of a triangle.
