Recent content by EsmeeDijk

Homework Statement We now specify the velocity v to be along the positive x1-direction in S and of magnitude v. We also consider a frame \overline{S} which moves at speed u with respect to S in the positive x1-direction. question 1 : Write down the transformation law for p^\mu . question 2...

Homework Statement We have the following orthogonal tensor in R3: t_{ij} (x^2) = a (x^2) x_i x_j + b(x^2) \delta _{ij} x^2 + c(x^2) \epsilon_ {ijk} x_k Calculate the following quantities and simplify your expression as much as possible: \nabla _j t_{ij}(x) and \epsilon _{ijk} \nabla _i...

Yes of course, I got 9b^2x_i x_j (x_k)^2 - 3b^2 x_i x_k x^2 \delta _{kj} - 3bc x_i x_k x_n \epsilon _{kjn} - 3b^2 x_k x_j x^2 \delta _{ik} + b^2 \delta _{ik} \delta _{kj} x^4 + bc x_n x^2 \delta _{ik} \epsilon _ {kjn} - 3bc x_k x_j x_m \epsilon _{ikm} + bc x_mx^2 \delta _{kj} \epsilon _{ikm} +...

Homework Statement I have a tensor which is given by t_{ij} = -3bx_i x_j + b \delta_{ij} x^2 + c \epsilon_{ijk} x_k And now I am asked to calculate (t^2)_{ij} : = t_{ik} t_{kj} Homework EquationsThe Attempt at a Solution At first I thought I had to calculate the square of the original...

Homework Statement A tensor t has the following components in a given orthonormal basis of R3 tij(x) = a(x2)xixj + b(x2) \deltaij x2 + c(x2) \epsilonijk xk (1) where the indices i,j,k = 1, 2, 3. We use the Einstein summation convention. We will only consider orthogonal transformations...