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Demos

The bogie of a railroad car is a multibody system connected with springs and dampers.
The parts (basically wheels, axis, and frame) respond to outer impact.
The motion of the multibody system obeys a dynamical law, and can be calculated by means of numerical methods.
The quality of the response essentialy depends on the speed *v* of the bogie.
The program (written in FORTRAN) calculates and plots the dynamics.
The speed *v* can be chosen freely.
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Response to an initial pertubation, depending on the speed *v* [km/h].

*v*=220 : stationary motion survives (1,1 MB mpeg)

*v*=260 : periodic motion takes over (1,2 MB mpeg)

*v*=650 : somewhat irregular (1,5 MB mpeg)

See also example exd10 and hassard's worksheet.

### Dancing balls

A ball under gravity is attracted by the minima of the surrounding landscape.
Here we have a valley with a hillock in the middle.
Clearly the top of the hillock is a repellot for the ball.
Depending on the initial state (coordinate *x* and velocity *v*) the ball choose
a trajectory towards one of the two stable attractors / minima.
Close initial states may end up in different attractors! (Example: compare *x=1*, *v=1* with *x=1*, *v=1.001*).
The motion of the ball may be seen as a symbol for more complicated dynamics.

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This model (Scheurle/Seydel 1999) models the dynamics of numbers of students over a time period of 40 semesters.
The dynamics varies with the number of freshmen.
In the model, one group of students studies a special field (red curve), all other students are represented by the yellow curve.
(The program is written in FORTRAN.)

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