Bounce_abg.tex

MTT command:

mtt Bounce abg tex

Figure 1.1: System Bounce: acausal bond graph

The acausal bond graph of system Bounce, togehter with a schematic diagram is displayed in Figure 1.1 (on page ) and its label file is listed in Section 1.1.1 (on page ). The subsystems are listed in Section 1.1.2 (on page ).

The model uses the CSW switched C element to simulate contact with the ground. The corresponding switching function (See Section 1.5), is based on the height above the ground $h$ as follows:

$$i_{sw} = \begin{cases}0 & \text{if $h > 0$}\\ -1 & \text{if $h \le 0$} \end{cases}$$ (1.1)

In other words, the component acts as an ideal spring when the ball is in contact with the ground yet has no effect when the ball is not in contact with the ground.

The ball is modelled as a point mass (the I component) and a linear resistance to motion (the (the R component).

The system was simulated for 100 time units and the resultant height is plotted in Figure 1.4. The ball was released at zero velocity from a height of ten units. The bounce height decreases due to the effect of the modelled air resistance.