Introduction

The math used in the com-pac package is based on the following description from the textbook "Microwave Molecular Spectra" by Walter Gordy and Robert L. Cook, page 12:

Quote

The classical angular momentum of a rigid system of particles

\[ \mathbf{P} = \mathbf{I} \cdot \omega \]

where \(\omega\) is the angular velocity and \(\mathbf{I}\) is the moment of inertia tensor which in dyadic notation is written as

\[ \begin{split} \mathbf{I} = & I_{xx} \mathbf{i} \mathbf{i} + I_{xy} \mathbf{i} \mathbf{j} + I_{xz} \mathbf{i} \mathbf{k} \\ & + I_{yx} \mathbf{j} \mathbf{i} + I_{yy} \mathbf{j} \mathbf{j} + I_{yz} \mathbf{j} \mathbf{k} \\ & + I_{zx} \mathbf{k} \mathbf{i} + I_{zy} \mathbf{k} \mathbf{j} + I_{zz} \mathbf{k} \mathbf{k} \\ \end{split} \]

with

\[ \begin{split} & I_{xx} = \sum{m (y^2 + z^2)} \\ & I_{yy} = \sum{m (z^2 + x^2)} \\ & I_{zz} = \sum{m (x^2 + y^2)} \\ & I_{xy} = I_{yx} = - \sum{m x y} \\ & I_{zx} = I_{xz} = - \sum{m x z} \\ & I_{yz} = I_{zy} = - \sum{m y z} \\ \end{split} \]

in which \(m\) is the mass of a particular particle and \(x, y, z\) are its positional coordinates relative to a rectangular coordinate system fixed in the body and with its origin at the center of gravity of the body. The summation is taken over all the particles of the body. The origin of the coordinate system is chosen at the center of mass because this choice allows the total kinetic energy to be written as ... [to be continued]