Dot product, cross product rearranging

[Jamalien]

Does anyone have an idea how to just simply rearrange for theta_dot_2 here? I know about triple cross product, circularity law etc, but can't seem to figure this out. (Perhaps it isn't possible?)

 

[topsquark]

If you know what the r's are then you can "rotate out" the [math]\dot{ \theta _2}[/math] to the left and then take the dot product. That will get you the magnitude [math]\dot{ \theta _2 }[/math] and it seems that you know that it's in the [math]\hat{i}[/math] direction so you have it. If [math]\dot{ \theta _2 }[/math] had more than one component we couldn't do this.

Also, the notation. Are the r's displacements? Unit vectors? Are i and k the unit vectors in the x and z directions, respectively? Please indicate the vectors when you write the equation. It saves trouble in the long run and it's a good habit to get into anyway.

-Dan