Tensor derivative in continuum mechanics

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The discussion focuses on the definition and implications of tensor derivatives in continuum mechanics, specifically referencing the Wikipedia article on the topic. The user seeks clarity on the relationship between tensor derivatives and covariant derivatives, expressing confusion about their physical and mathematical significance. It is established that tensor derivatives are distinct from covariant derivatives and relate more closely to directional derivatives in vector spaces. The conversation highlights the need for a deeper understanding of how connections influence tensor behavior.

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  • Knowledge of covariant derivatives
  • Basic concepts of vector spaces
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enricfemi
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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 )
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.
 
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in other words, if we have a connection, how it acts on tensors.
 
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.
 

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