VPOD 3DOF Vibratory Device

Last modified 11 September, 2009

Nondimensional 3DOF Bouncing Ball Simulator

The Nondimensional 3DOF Bouncing Ball Simulator is a simple Matlab program meant to mimic the behavior of a bouncing ball on a vibratory device capable of sinusoidal motion in three degrees, such as the VPOD. The simulator uses a numerical method in which the equations of motion describing the ball's flight are determined from the state variables of the previous impact. The program uses a binary search to locate the time at which the ball's position in the x,z plane is equal to that of the oscillating bar. In short, it calculates the intersection of a parabola with a sinusoid, uses a simple impact model to compute the new state variables, and repeats this computation as many times as desired. The equations of motion for the oscillating bar are as follows:

$x(t)=A_{x}sin(\omega _{x}t+\phi _{x})\,$

$z(t)=A_{z}sin(\omega _{z}t+\phi _{z})\,$

$\theta (t)=A_{\theta }sin(\omega _{\theta }t+\phi _{\theta })\,$

Download the simulator.