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Question: Implicit differentiation for matrices

I am trying to reproduce some systems for multibody systems by using maple.

I want to define a rotation matrix

Rot__alpha:=Matrix([[ cos(alpha) , -sin(alpha) , 0 ], [ sin(alpha) , cos(alpha) , 0 ], [ 0 , 0 , 1 ]]);

Now I want to differentiate this matrix with respect to time t. I have tried the following but it does not work:

map(implicitdiff, Rot__alpha,alpha);

I actually want something like this:

d/dt (Rot(alpha))=Matrix([[ -sin(alpha)*a , -cos(alpha)*a , 0 ], [ cos(alpha)*a , -sin(alpha)*a , 0 ], [ 0 , 0 , 0 ]]);

where a is d(alpha)/dt. So alpha is not an explicit function of t.

It would be great if someone could provide me a method for performing these kind of calculations. 
           

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