General rule product matrices?

[Yoran91]

Hi everyone,

I'm trying to find a general rule that expresses the product of two rotation matrices as a new matrix.
I'm adopting the topological model of the rotation group, so any rotation which is specified by an angle $\phi$ and an axis $\hat{n}$ is written $R(\hat{n}\phi)= R(\vec{\phi})$.

So, given two rotation matrices $R(\vec{\phi}_1) , R(\vec{\phi}_2) \in SO(3)$, what can be said about the product $R(\vec{\phi}_1)R(\vec{\phi}_2)$?

What is are the axis and the amount of degrees that specifies this rotation matrix?

 

[tiny-tim]

Hi Yoran91!

See http://en.wikipedia.org/wiki/Quaternions_and_spatial_rotation