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osnarf

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Edit - maybe I have the notaton figured out now and am just confused.

The below relevant quotations come from Landau and Lifgarbagez, volume 7 : The theory of elasticity, chapter 1.

Page 2:

Page 5 (last paragraph):

In quotation 2 - where did D come from? What is it?

In quotation 3 - Is he using Einstiein summation notation still, because I don't understand why there would only be two components of the force, or two co-ordinates, because everything so far as been 3 dimensional. I don't understand how this is the moment tensor (it does make sense if its done for all 3 2d planes (xy, yz, zx), and F

Thanks for your help.

## Homework Statement

The below relevant quotations come from Landau and Lifgarbagez, volume 7 : The theory of elasticity, chapter 1.

**2. Relevant quotations**Page 2:

where uequation 1.2

dl'^{2}= dl^{2}+ 2u_{ik}dx_{i}dx_{k}

_{ik}is the strain tensor, dl is the original distance between two points, and dl' is the deformed distance between the two points. x_{i}are co-ordinates.^^^Where, in the book, D is a squigly d (lower case delta?). Looks like the d used in variations.Like any symetrical tensor, u_{ik}can bediagonalisedat any given point.

...

If the strain tensor is diagonalised at any given point, the element of length (1.2) near it becomes:

dl'^{2}= (D_{ik}+ 2u_{ik})dx_{i}dx_{k}\

= (1 + 2u^{(1)})dx_{1}^{2}+ (1 + 2u^{(2)})dx_{2}^{2}+ (1 + 2u^{(3)})dx_{3}^{2}

Page 5 (last paragraph):

Let us determine the moment of the forces on a portion of the body. The moment of the forceFcan be written as an antisymmetrical tensor of rank two, whose components areF, where_{i}x_{k}- F_{k}x_{i}xare the co-ordinates of the point where the force is applied._{i}

## The Attempt at a Solution

In quotation 2 - where did D come from? What is it?

In quotation 3 - Is he using Einstiein summation notation still, because I don't understand why there would only be two components of the force, or two co-ordinates, because everything so far as been 3 dimensional. I don't understand how this is the moment tensor (it does make sense if its done for all 3 2d planes (xy, yz, zx), and F

_{i}is a component of force in the*i*direction, then it's a scalar returned for the norm of the moment, directed in the direction normal to the plane - but then you get either a 2nd order diagonal tensor, or a first order tensor, neither of which is an antisymmetrical tensor of rank 2)Thanks for your help.

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