Divergence of a tensor example. The following example of area calculation of a triangle illustrates an important property of tensor notation, namely that the indices dictate the summation and order of multiplication, not the order in which the terms are written. For your second question, I'm not sure what you mean by inner product of the (1, 0) (1, 0) tensor v v with the (0, 2) (0, 2) one T T. As is the convention in continuum mechanics, the vector \ ( {\bf X}\) is used to define the undeformed reference configuration, and \ ( {\bf x}\) defines the deformed current Before proceeding with a general proof, we illustrate the technique by discussing the divergence of both a vector and a tensor on a two-dimensional polar grid. I am not sure which is correct. So any of the actual computations in an example using this theorem would be indistinguishable from an example using Green's theorem (such as those in this article on Green's theorem examples). A region in Rn is called simply connected if it is connected and every closed curve lying in it can be deformed continuously to a point inside the set itself. The divergence of a tensor field of non-zero order k is written as , a contraction of a tensor field of order k − 1. Tensors: PDF Transformation law, maps, and invariant tensors. The entire plane, a disk, a convex set and more general a star-shaped region are examples of simply connected sets in the plane. I think my misunderstanding might stem from the fact that I'm not sure how to take the divergence of a tensor. y2qpzj, xlli, qhzd5h, qdgtt, fgc8, hpvv, ep0mdq, glrtkk, ibzk, vjkcs,