BouncingRod_abg.tex

MTT command:

mtt BouncingRod abg tex

Figure 2.1: System BouncingRod: acausal bond graph

The acausal bond graph of system BouncingRod is displayed in Figure 2.1 (on page ) and its label file is listed in Section 2.1.1 (on page ). The subsystems are listed in Section 2.1.2 (on page ).

The system consists of a uniform rod of mass 1kg, length 2m (and therefore of inertia about the mass centre of $\frac{1}{3}$   kgm$^2$. The rod is released at an angle of $\frac{\pi}{4}$ from the vertical, the mass centre is $10$m above the ground and all velocities are initially zero. The gravitational constant is taken as unity.

The ground is modeled as an ideal compliance in the vertical direction with compliance of $0.1$   mN$^{-1}$ and it is assumed that contact takes place at the rod tips only. There is no horizontal resistance to motion. This idealised setup is modeled by a two CSW components, one for each rod tip, modulated by the height of each rod tip above the ground: each CSW is off when the corresponding height is positive.

The system was simulated for 100 time units and the resultant height of each tip is plotted in Figure 2.5. The rod was released at zero velocity from a height of ten units and at an angle of $\frac{\pi}{4}$ radians to the vertical. The oscillations in height are due to rod rotation about its mass centre. The bounce height changes due to energy transfer to and from the rod rotation about its mass centre.