0                 0                  0                  0                  0
  $\dot{w}$                   0                 0                    0                  0           0           2              0                0                 0                  0                  0                  0
  $\dot{\varphi}$             0                 0                    0                  0           0           0           $2v ^2$             0                 0                  0                  0               $2v ^2$
  $\dot{\chi}$                0                 0                    0                  0           0           0              0              $2u^2$              0                  0                  0                $4u^2$
  $\dot{\vartheta}$           0                 0                    0                  0           0           0              0                0              $2 w^2$               0                  0               $6 w^2$
  $q_1$                       0                 0                    0                  0           0           0              0                0                 0           $\mathcal{ J}_1$          0                  0
  $q_2$                       0                 0                    0                  0           0           0              0                0                 0                  0           $\mathcal{ J}_2$          0
  $q_3$                       0                 0                    0                  0           0           0            $2v^2$           $4u^2$           $6w^2$                0                  0           $\mathcal{ J}_3$

  : \[T:1\] The matrix of inertia $\mathcal{ G}$ after the introduction of the variables $u_0$, $v$, $u$, $w$, $\varphi$, $\chi$, and $\vartheta$ (see text). Here, $\mathcal{ J}_1 = \mathcal{ J}_2 = 3(\beta_2^2 + 2\beta_3^2)$, and $\mathcal{ J}_3 = 4 f^2(\beta_2,\beta_3)
  \ u_0^2 + 
  2v^2 + 8u^2 + 18w^2$. Only the leading terms are shown. Neglected terms are small of the first order (or smaller) in the sub-matrix involving only $\dot{\beta_2}$, $\dot{\beta_3}$, $\dot{u_0}$, $\dot{v}$, $\dot{u}$, $\dot{w}$, $q_1$ and $q_2$; of the third order (or smaller) in the sub-matrix involving only $\dot{\varphi} $, $\dot{\chi}$, $\dot{\vartheta}$ and $q_3$; of the 