Homework #6
Feel free to use
http://www.continuummechanics.org/interactivecalcs.html when applicable.
Use the following deformation gradient for the problems.
\[
{\bf F} =
\left[ \matrix{
\;\;\; 1.5 & \;\;\; 0.3 & 0.2 \\
0.1 & \;\;\;1.2 & \;\;\; 0.1 \\
\;\;\; 0.3 & 0.2 & \;\;\; 1.1
} \right]
\]

Determine \({\bf R}\) and \({\bf U}\) in \({\bf F} = {\bf R} \cdot {\bf U}\).
Do it the hard way by multiplying all the matrices out yourself (but not by hand! use software).
Then check your result using this page:
http://www.continuummechanics.org/techforms/RUDecomposition.html

How many degrees of rigid body rotation are in this deformation gradient, and
what is the axis of rotation?

Now that you have \({\bf R}\) and \({\bf U}\) from #2, calculate \({\bf V}\) and use
http://www.continuummechanics.org/techforms/VRDecomposition.html
to check that you got it right.