This project is a collaboration between me and my friends Shawn Duan (WashU '25) and Victor Kao (UIUC '24), and it integrates software development and physics integration. 

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The app is developed in Xcode, Apple's development environment. Even though apple has a physics package within its developer API, we decided not to use it as it does not model the physics we need adequately sometimes. We coded the physics and from scratch using the Verlet Integration method. 

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Put simply, Verlet Integration is an implementation of Newton's equations of motion, especially ones relating position, velocity, and acceleration (1). By using a Taylor expansion for an incremental step in time forward and backward, we obtain 2 expanded equations that we can add together to cancel out velocity (2,3). The final form of the motion equation only has position and acceleration terms (4). This is only a brief explanation; to see a fuller explanation please click here. 

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Techniques like this can be seen frequently and clearly in functions like Simulate(), AdjustCollisions(), and ApplyConstraint() in Rope.swift. 

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The collision between the ball and the rope is further developed by our own techniques, with tunable parameters that model the stiffness and elasticity of the string.