Course Solutions Uncategorized (Solved) : B Rate Change Rotating Vector Using Matrix Representation 3 Points Total Ve Argued Previou Q33248713 . . . .

(Solved) : B Rate Change Rotating Vector Using Matrix Representation 3 Points Total Ve Argued Previou Q33248713 . . . .

 

B. Rate of change of a rotating vector using the matrix representation (3 points total) Weve argued previously that for rotation about a fixed axis υ, any vector v that is fixed in the body frame changes in the inertial space frame with the time dependence dt where Lets show this also follows directly from the matrix representation of the rotation We can assume our system starts rotating about direction υ at time t 0, so that 0(t= 0) = 0 Then the time-dependent vector V(t) has the column-vector representation v(t) -R(0(t), u) v(0). By the Chain Rule we have d6 where the derivative of the matrix dR/d0 is found by differentiating each component. Now lets just apply the definition of the derivative: Rim. lim A0 lim - u1

B.

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