Simulating 2D Collusion Dynamics of Two 3D Spherical Objects

Written as an example for Sophomore engineering students (KHAS University, Istanbul) in Spring semester (2023), for educational purposes.

% This model is for educational & numerical experimentation purposes only.

% It assumes that two spheres, either rolling on a boundary or moving

% freely in space, are in collusion course . Therefore, when the user

% disables the "boundary", the function also disables gravity and fluid

% drag, automatically. All physical calculations are carried out based on

% assumptions and available data. Better assumptions might yield more

% realistic results.

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% Contact phenomena is modeled with the help of Hertzian contact of

% spherical objects of arbitrary dimensions even though the source material

% explains the said approach exclusively for interacting micro-objects.

% Automatic dimensional scaling for applied force(s) and simulation time is

% not implemented. Contact friction is based on stiction and Coulomb

% friction.

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% There are several material/geometry properties that can be changed and/or

% tuned. In this version, the spheres are assumed to be made out of steel

% whereas the boundary is assumed to be of wood.

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% Changing the magnitude of the external forces applied on the spherical

% objects will cause a different trajectory and a different view area (for

% the animation.) due to collusion dynamics. It is also observed that if a

% lighter but larger spherical object was to be hit by a heavier & smaller

% one hard enough, the model is able to predict that it might be launched

% up in the air, as a result.

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% The frame-rate of the animation is dependent on the size of the solution

% object; therefore, the speed of the animation does not seem to be

% regular at all times.

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% Tested in Windows only.