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Matrix/Tensor derivative for Stress Tensor

asked 2011-05-18 10:20:46 -0500

packoman gravatar image

updated 2011-05-18 20:47:46 -0500

I need to do define/calculate the following stress tensor in an elegant way:

$T_{i,j} := -p \delta_{i,j} + \eta (\partial_i v_j + \partial_j v_i)$

where i,j can be x,y,z and

$\partial_i v_j := \frac{\partial v_j}{\partial i}$

I've found the sage-function kronecker_delta for the first term, but I am having problems with the two partial derivatives.

Thanks in advance!

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Can you post what have you tried, or what are exactly your problems? The `diff` function can compute partial derivatives: just pass the variable with respect to you are differentiating. Does this help you in any way?

Juanlu001 gravatar imageJuanlu001 ( 2011-05-20 23:19:13 -0500 )edit

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answered 2015-05-23 17:37:51 -0500

roberto gravatar image

Have you tried SageManifolds? sagemanifolds.obspm.fr

I do tensor calculus with it and I think it's good. Then as Juanlu001 already told you try to use diff and post your code.

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Asked: 2011-05-18 10:20:46 -0500

Seen: 666 times

Last updated: May 23 '15