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Math Help - Continuum Mechanics/Elasticity help re: Polar Decomposition Theorem

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    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.
    Last edited by mr fantastic; January 7th 2012 at 05:19 PM. Reason: Merged posts.
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