1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Tensor calculus, gradient of skew tensor

  1. Aug 19, 2014 #1
    Hi there. I was dealing with the derivation on continuum mechanics for the conservation of angular momentum. The derivation I was studying uses an arbitrary constant skew tensor ##\Lambda##. It denotes by ##\lambda## its axial vector, so that ##\Lambda=\lambda \times##

    Then it defines ##w(x)=\lambda \times r=\Lambda r##

    So that ##grad (\Lambda r)=\Lambda##

    And thats the doubt I have.

    When I do ##grad (\Lambda r)## I have (I use that ##r=x-x_0##):

    ##\displaystyle grad (\Lambda r)=\frac{\partial}{\partial x_k} ( \Lambda_{ij} r_j ) = \frac{\partial \Lambda_{ij} } {\partial x_k} r_j + \frac {\partial r_j} {\partial x_k} \Lambda_{ij} = \frac{\partial \Lambda_{ij}} {\partial x_k} (x_j-x_{0j})+\frac{\partial (x_j-x_{0j})}{\partial x_k}\Lambda_{ij}=(grad \Lambda ) r+\Lambda ##

    Now, the fact that ##\Lambda## was constant determines that the gradient is zero? that was the doubt, I recognize that I didn't noticed before the fact that the tensor was constant until I written this post :p
     
    Last edited: Aug 19, 2014
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?



Similar Discussions: Tensor calculus, gradient of skew tensor
  1. Tensor calculus (Replies: 0)

  2. Tensor calculus (Replies: 0)

  3. Tensor Analysis (Replies: 0)

  4. Mixed Einstein tensor (Replies: 0)

Loading...