# tensor

1. ### Inertial "moment" of a solid given an inertia tensor

Hi all, I am programming some software computing inertial forces of some moving structure. So far, the structure have been represented as a cloud of mass points. For each mass point, inertial forces are computed using some formulas like in this article...
2. ### Stress energy tensor transformation

Show that if you add a total derivative to the Lagrangian density L \to L + \partial_\mu X^\mu, the energy momentum tensor changes as T^{\mu\nu} \to T^{\mu\nu}+\partial_\alpha B^{\alpha\mu\nu} with B^{\alpha\mu\nu}=-B^{\mu\alpha\nu}. (Note: the Lagrangian can depend on higher order derivatives...
3. ### What causes rotation in the Navier-Stokes Equation?

It is known that rotation in the flow results from the viscous terms in the Navier-Stokes (N-S) equation. However, when deriving the N-S equation from the general principle of linear momentum in Continuum Mechanics, we use the constitutive relation for isotropic Newtonian fluids which states...
4. ### Tensor calculation in Lorentztransformations

Hi, I have difficulties understanding the following relations. Given the Minkowski metric \eta_{\alpha\beta}=diag(1,-1,-1,-1) and the line segment ds^2 = dx^2+dy^2+dz^2, then how can i see that this line segment is equal to ds^2 = \eta_{\alpha\beta}dx^\alpha dx^\beta . Further, we want the...
5. ### Lagrangian Mechanics - metric tensor

I am trying to follow the derivation of the Noether's theorem with respect to a complex wave on a guitar string. My text obtains the Lagrangian: [TEX]\mathcal{L}=\frac 12 (\partial_\mu \chi^*)(\partial^\mu \chi)[\TEX] In deriving this Lagrangian density in classical mechanics is the...
6. ### Strain tensor

Hi folks, An apparently simple question about the strain tensor I cannot figure out myself though... Tensors are said to be "objects" that accomplish a linear mapping between two vectors. The moment of inertia tensor, for instance, relates the angular momentum to the angular velocity. In...
7. ### Tensor Calculus Proof

Hi, I am studying tensor calculus and I am not too familiar with tensors currently. The question I have is: The steps to prove that a lie derivative satisfies the usual product rule, ie it is Leibniz. Please see my attachment that shows where I am up to. It is much easier to scan this than...
8. ### Questions for dielectric tensor

1. About the dielectric tensor in 1-dimensional semiconductors: it seems that the tensors should be diagonal, but what about the array of such system? should we expect an isoptropic behavior? 2. Suppose we have the born effective charges of such a system, how can we get the dielectric tensor...
9. ### Weyl tensor dynamic

I recently became interested in relativity, therefore, I got me some good books on the subject and have decided to self-study as I find time. Anyway, has anyone ever seen the sci-fi/horror movie Event Horizon?. In the beginning, the man who developed the drive which propels the ship by...
10. ### Classiscal Mechanics: Inertia Tensor

A rigid body consists of three equal masses (m)fastened at the position (a,0,0), (0,a,2a), and (0,2a,a). Find the inertia tensor I. Find the principal moments and a set of orthogonal principal axes. What I have done so far is use the positions to draw a pictorial representation. Then I tried...