Tensor derivative in continuum mechanics

1. Feb 22, 2010

enricfemi

i am currently reading a book about continuum mechanics. they define derivatives of tensor valued functions of tensors in such way:
http://en.wikipedia.org/wiki/Tensor_derivative_(continuum_mechanics [Broken])
it seems to be related covariant derivative, but i can not figure out its meaning in physics or maths.
i just try to understand why it should be defined in such way.
any talk will be appreciate.

Last edited by a moderator: May 4, 2017
2. Feb 23, 2010

enricfemi

in other words, if we have a connection, how it acts on tensors.

3. Feb 24, 2010

enricfemi

ok, it has nothing to do with covariant derivative, seems to be some kinds of direction derivative in vector space. still unware of its meaning.