The 6-DOF translational equation along the \(x\)-axis is
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The translational equations of motion in body axes are
\[
\boxed{
\begin{aligned}
X&=m(\dot{u}+qw-rv),
Y&=m(\dot{v}+ru-pw),
Z&=m(\dot{w}+pv-qu).
\end{aligned}
}
\]
The rotational equations involve the moments \(L,\ M,\ N\).