# General rule product matrices?

1. Jun 4, 2013

### 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?

2. Jun 6, 2013