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:
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x(t) = A_xsin(\omega_xt+\phi_x)\, }
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle z(t) = A_zsin(\omega_zt+\phi_z)\, }
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \theta(t) = A_\theta sin(\omega_\theta t+\phi_\theta)\, }
