Thread: Continuum Mechanics/Elasticity help re: Polar Decomposition Theorem

That is a model question. b) is just stating the theorem, which is as follows in my notes:

If a linear transformation F is invertible with det F > 0, then there exists unique symmetric positive-definite linear transformations U and V, and a unique proper orthogonal transofrmation R, such that:

RU = F = VR.


I'm just having a bit of trouble applying the theorem, specifically "Show that the deformation can be considered to be the result of three simple stretches followed by a rotation. Explain the precise nature of the stretches and rotation.

Looking through the printed and my written notes, it revolves around the homogeneous deformation:

x = A + H(X - A)

Anyone know much about this stuff?

Also, I wasn't quite sure if this was the correct forum. The Elasticity course I take is heavily reliant on Linear Algebra.