Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Three-Body Inertia Tensor   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 $m_a/a=m_b/b=m_c/c=\rho$, 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 $I=\rho abc$, 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.

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The categories of this paper are: mtrl-th
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The categories of this paper are: funct-an
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The categories of this paper are: solv-int
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The categories of this paper are: quant-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-th
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The categories of this paper are: stat
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The categories of this paper are: plasm-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: eess
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The categories of this paper are: nlin
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The categories of this paper are: hep-ex
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The categories of this paper are: q-bio
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The categories of this paper are: q-alg
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The categories of this paper are: adap-org
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The categories of this paper are: chem-ph