Recent content by Mike_bb

Could you explain how to derive this formula?

fresh_42 martinbn Big thanks!! :smile:

I'm not sure if it's so but the book uses such terms as "very small element f" = "infinitesimal element f" in context of vector ##V## circulation on element f. Perhaps it's the reason why we say about tangent vector as approximation of vector ##V## in infinitesimal scale of element f (or...

You missed one thing that I wrote in post #1. I mentioned about Taylor series as it was written in the book.

The book doesn't use such terms as "tangent space" and "manifold" quite. The book contains a chapter that is devoted to an introduction to vectors and that's all.

Russian book "Theory of electricity". https://scask.ru/k_book_tel.php?id=19 page 38

Hello! In one book I saw that function ##V## of 3 variables ##V_x, V_y, V_z## (vector field in 3D) can be decomposed in a Taylor series without higher-order terms (partial derivative of second power and higher) at point ##(0,0,0)## such way: I think so: higher-order terms can be neglected...

It's interpreted as ##(\partial v_x/\partial y)\vec{\hat{x'}}##

I computed projections of curl in new coordinate system (yz-plane is rotated by an angle 45 degrees about x-axis) using this formula: ##cos(n, x)## is cosin of angle between normal vector in new coordinate system(yz-plane is rotated by an angle 45 degrees about x-axis) and x-axis in old...

Projections of curl can be calculated using this formula: I substituted values of curl projections (post #1) in this formula and obtained wrong result (for x', y', z'). I don't understand why. Could anyone know what's wrong?

No. It's not my problem. I just want to calculate projection of curl on x',y',z' directions using contour rotation in coordinate system.

Hello! I tried to calculate projections of curl using rotation of coordinate system but I encountered with following problem. Given: ##rot_xA=\frac{\partial A_z}{\partial y}-\frac{\partial A_y}{\partial z}=0## ##rot_yA=\frac{\partial A_x}{\partial z}-\frac{\partial A_z}{\partial x}=1##...

Solved:

What does expression exist for this case? If we know only Sigma1 tensor then how to find Sigma2 tensor?

Hello ! I derived equations of stress tensor 2D transformation. Some details: I have plane ABCD in two cases (see top on the pic) and I know tensor components for case 1 only. Only plane ABCD rotate in two cases (top of the picture) but not coordinate system. Coordinate system rotates only on...