Mathematical Modeling by Christof Eck Harald Garcke & Peter Knabner

Author:Christof Eck, Harald Garcke & Peter Knabner
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

with a translational vector and an orthogonal matrix Q. We have

(5.37)

As both coordinate systems are positively oriented, we have .

Fig. 5.9Observer change

In the following we assume that and Q are as functions of t smooth enough. The coordinates x and are interpreted as Eulerian coordinates over the same reference domain, i.e., (Fig. 5.9)

We have

The velocities , in Eulerian coordinates which belong to these coordinates are defined via

With this we obtain

(5.38)

The last identity follows with the help of

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