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Identity in continuum mechanics
For a problem in the textbook I am reading, I need to prove that $\int_Vw_{i,j}v_jdV = \int_Sw_iv_jn_jdS$, where $S$ is the boundary of the volume $V$, $v_i$ is the velocity vector field of a ...
- 1,008
1
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Metric and Convariant Tensor
$g_{ij}$ is the metric tensor. Show that $g^{ij}$ which satsifies $g_{ij}g^{jk}=\delta_i^k$ is a covariant tensor of rank $2$.
I am not sure how to show this? Does it instead mean to show that $g_{ij}...
- 1,019
1
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1
answer
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Tensor notation of a triple scalar product
I want to write the tensor notation for $$[a\dot\ (b\times c)]a=(a\times b)\times (a\times c).$$
What I got so far is:
$$a \dot\ (b\times c)=a_i(\epsilon_{ijk}b_jc_k)=\epsilon_{ijk}a_ib_jc_k.$$ Now ...
- 1,019