The direction cosine matrix of a body determined using Euler angle is given below: A=\left[\begin{array}{ccc} 0.6667 & -0.3333 & 0.6667 \\ 0.6667 & 0.6667 & -0.3333 \\ -0.3333 & 0.6667

& 0.6667 \end{array}\right] At the given configuration, the body has an instantaneous angular velocity defined by the vector \omega=\left[\begin{array}{lll} 110 & 90 & 0 \end{array}\right]^{T} \frac{\mathrm{rad}}{\mathrm{s}} . \text { Find the time derivatives of the Euler angles. }