Simultaneous Collisions in Various Numbers of Dimensions
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Description
The project is a continuation of research conducted by students in the summers of 2017 and 2018, which dealt with hierarchical systems of collisions of many balls. However the current project focuses on simultaneous collisions of balls, i.e., situations where more than two balls collide, each with each other, at the same time. The simultaneity condition requires much more complicated mathematical treatment to ensure the physical principles of conservation of momentum and energy are satisfied. We study the collisions in 2D, 3D, and 4D. We have developed a novel computational approach that combines hand computations and MATLAB symbolic computations with computer simulation. We have developed several web-based, interactive computer programs that determine the balls’ behavior during simultaneous collisions and visualize their motion. The programs are written in Javascript, with CSS and HTML components and use the Three.js API (application programming interface) and library of 3D routines.
Simultaneous Collisions in Various Numbers of Dimensions
The project is a continuation of research conducted by students in the summers of 2017 and 2018, which dealt with hierarchical systems of collisions of many balls. However the current project focuses on simultaneous collisions of balls, i.e., situations where more than two balls collide, each with each other, at the same time. The simultaneity condition requires much more complicated mathematical treatment to ensure the physical principles of conservation of momentum and energy are satisfied. We study the collisions in 2D, 3D, and 4D. We have developed a novel computational approach that combines hand computations and MATLAB symbolic computations with computer simulation. We have developed several web-based, interactive computer programs that determine the balls’ behavior during simultaneous collisions and visualize their motion. The programs are written in Javascript, with CSS and HTML components and use the Three.js API (application programming interface) and library of 3D routines.