Also, guten Morgen, mein Name ist Paul.

Also, I remember well, we stopped here at the balance phase.

Okay, so here everything that we said earlier should somehow come together according to the phase.

So we have the usual balance equation for mass, linear momentum, linear momentum, and later also balance equation for energy and entropy.

And I think we have already defined the polar mass as the integral over the mass density over the integration of the linear momentum.

So, as you can see, the mass density, you can express that polar mass in two ways.

In 2008 by a Jacobian determinant as usual and then in the case of the mass balance, indeed the conservation of mass, the statement is that whatever mass has been there in a certain domain, this won't change the time.

So, the time derivative for the mass is zero and from this by localization we can obtain this point by statement that the time derivative of the mass density per unit volume is also the definition of time.

And that in turn means that the mass density for deformation per unit volume for deformation does only depend on the phase variables and not on the time variables.

So we can describe bodies that have different mass density, zero from two points to the other, but at each point the mass density does not change over time.

So, the time derivative of the mass density is zero. Since the two rows are connected today, we can put the time derivative on top of this quantity, which is largely approximately on the right-hand side, so we get a expression for the change of the two rows of two.

This is the same as here. So, in this notation for the DT, the time derivative of the mass density per unit volume and the form does not change.

We can multiply that simply by the time derivative of the phase. No excitation here in the sense that we have this relation between the time derivative of the phase and the time derivative of something.

And the army is then in this box here. So the time derivative of the mass density per unit volume and the forming of the different bodies depends on their use and that is given to the time derivative of the time velocity,

which is already the definition of the momentum density. This is the workings of the momentum density of the wave-density range of the density.

This is the time derivative here. This is the time derivative of the time derivative of the time velocity.

This is the time derivative of the time velocity. This is the time derivative of the time velocity.

This is the time derivative of the time derivative of the time velocity.

So we can also understand that how the V is related to the V, is related to the little v, to the real velocity by using this parallel relation between the time derivative and the space time derivative.

So to think that why the inverse deformation methods essentially in this important specialization they don't change, they are made by the Euler theory.

And then you get this relation between the time derivative of the time velocity, this gradient here is our inverse deformation gradient, you can get the relation between the time of the little v and the time of the little epsilon pole.

So this is the time derivative of the time velocity.

So the message here was that regardless of which parallel equation we look at, we can come up with essentially four different formats that are related by the Euler transformation, which is also down here in the transfer field.

So this is the time derivative of the time velocity.

So this is the time derivative of the time velocity.

So the linear momentum and balance has to do with the definition of the linear momentum, which is mass density in terms of velocity, mass density in terms of velocity.

So these are the two different versions, sub 0 and sub 10, which differ through the volume 4 and the faster definition.

So if you define the total linear momentum that is contained in the momentum in the zero, and call the upper case t here, then the total linear momentum is the time derivative of the momentum.

So this is the time derivative of the time velocity.

So this is the time derivative of the momentum.

So this is the time derivative of the time velocity.

So this is the time derivative of the time velocity.

So this is the time derivative of the time velocity.

So this is the time derivative of the momentum.

So this is the time derivative of the time velocity.

So this is the time derivative of the time velocity.

So this is the time derivative of the momentum.

So this is the time derivative of the momentum.

So this is the time derivative of the momentum.

So this is the time derivative of the momentum.

So this is the time derivative of the momentum.

So this is the time derivative of the momentum.

So this is the time derivative of the momentum.

So this is the time derivative of the momentum.

So this is the time derivative of the momentum.

So this is the time derivative of the momentum.

So this is the time derivative of the momentum.

So this is the time derivative of the momentum.

So this is the time derivative of the momentum.

So this is the time derivative of the momentum.