Mass matrix in (local) main axis coordinate frame

Consequently, the mass matrix becomes in the principal axis coordinates

$\displaystyle \boldsymbol{M} = \left[ \begin{array}{cc} \boldsymbol{M}_D & \boldsymbol{M}_{ND} \\ \boldsymbol{M}^T_{ND} & \boldsymbol{M}_D \end{array} \right]$

(37)

with

$\displaystyle \boldsymbol{M}_D = \frac{1}{3}(X_2 - X_1) \left[ \begin{array}{cc... ... 0 & 0 & \rho I_{22} & 0 \\ 0 & 0 & 0 & 0 & 0 & \rho I_{33} \end{array} \right]$

(38)

and

$\displaystyle \boldsymbol{M}_{ND} = \frac{1}{6}(X_2 - X_1) \left[ \begin{array}... ... 0 & 0 & \rho I_{22} & 0 \\ 0 & 0 & 0 & 0 & 0 & \rho I_{33} \end{array} \right]$

(39)