Is Your Rotation Matrix Correct?

[Art_]

Hello all,

I am having a problem with this question. Can not see what I am doing wrong.

Homework Statement

Show that the two expressions are equivalent, by construction a rotation matrix R^si.

S = (-R sin(a*a_dot) - w R sin(a))s₁ + (R cos(a*a_dot) + w R cos(a))s₂
I = (-R sin(a+wt)(a_dot+w))i₁ + (R cos(a+wt)(a_dot+w))i₂

Homework Equations

I=R^siS

The Attempt at a Solution

Then the rotation matrix should be

cos(wt) -sin(wt)
sin(wt) cos(wt)

or are the terms in the parenthesis are wrong?

Thank you for your help.
Art

 

[vela]

I assume t stands for time and the dot represents the derivative with respect to time. There seem to be several problems. For instance, in your expression for I, you have $\sin(a+\omega t)$. This implies a must be unitless, but in the line above, the argument of cosine, $a\dot{a}$, will then have units of 1/time, when it needs to be unitless.