What is a scaling rotation matrix? (old version)

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Thanks again for all of your work, in this entry I would like to ask for your help I have a doubt that is making me struggle and I have look at a few books but some of them don't mention this and in the best case they just give a few details and I need bit more.

I'm looking for matrix logarithm of rotations and if you could guide me in this giving me any advice, any paper I would be very thankful. The books that have helped me the most for this are: "Modern Robotics from Kevin Lynch" and "A Mathematical Introduction to Robotic Manipulation from
Richard M. Murray "

Thanks in advance c:

mr.es