So, good morning.

Good.

Last time the question came up if there is anyone sitting here who doesn't understand any German.

Okay, so how do we do it? Do you want to hear our further Danish or German?

I don't care. How does it look? Short vote.

Who would like to hear it in German?

There seems to be more. Okay. Good. Who doesn't care?

Okay. Good. I don't care either.

Okay, maybe again briefly as a follow-up. Last time we had thought about the definition of the rotation pulse,

how it would look like if the body is rigid, for such a rigid body.

And there we essentially used this representation for the speed field of such a rigid body.

This is a result from the third semester.

And then we used the representation of the rotation pulse of such a body.

You can see that in the first line up there.

And if you do that, then there is a term that falls out because of the definition of the center of gravity.

The first term here. And here is this two-fold product.

Last time there was a pre-direction rotor in the equation of this cross product.

And if you look at that in your notebook again, you may correct that.

I think last time we wrote it in a minus sign, pre-multiplicated.

But that's not quite right. The right answer is this one here.

So if you can understand that at this point, you would have to correct that again.

And especially down here at the index representation you can see that again.

As I said, these components belong in there as they are here.

So far written or perceived.

Well, then we started to deal with the Cauchy theorem.

Here you can see another picture of Cauchy.

And here I have another quote from a work by Cauchy from the 19th century.

And here he basically describes what is the Cauchy theorem for us.

So if you are the French might, you can recognize that.

Otherwise I'll translate it for you very roughly.

So that says the pressure or the thrust that is exerted on a level, on any level.

That would be this, you see, this slanted level with any normal N.

And that can be easily represented or derived both in the size and direction from the pressure or the thrust.

So that's what we call the tension vector now.

Which is exerted on three right-angled surfaces.

That's actually exactly what we are going to represent as a Cauchy theorem in a formula.

Yes, the good Cauchy.

So then we looked at this picture.

The central idea is, as already in the first semester, that one then basically divides a body in two parts.

And in this section then has to write correspondingly cut size.

So that each part for itself remains in the same weight in this case.

And here is now this entire cut size that then arises.

Sets together, if you want, from a distributed force per area.

And that's just these tension vectors, force per area.

So that the contribution of such a small surface element in this cut surface to the entire cut force is obtained from the tension vector at the point multiplied with the surface element.

So and then we had these surface normals introduced here.

To characterize the cut surface at the point completely.

Well, the total surface is here small a. The outer surface normals are n1, n2.

And we choose one of them as a reference norm, because they are exactly the opposite when I make a cut.

So I choose n1 as n here and then use it as normated to the length 1.