Hello,
My name is Joe.
12th grade student athlete at R.E. Mountain.
1.1 Double Pendulum
In this project, I find periodic trajectories of a double pendulum through calculations of the Lyapunov exponent at different drop angles. The result is a fractal-like heatmap that outlines the chaotic nature of the double pendulum.
You can read the paper here. Or, you could
1.2 Debate Motions Network
Debate is a field that interacts with a diverse range of topics. This project aims to use word embeddings to find cosine similarities and ultimately create an organization of debate motions in a network form, allowing for the ability of finding connections between motions that is not possible with the conventional folder structure of organization.
1.3 Periodic Three Bodies
The three-body problem is known for its chaotic nature. In this project, I developed a new algorithm to measure the periodicity of a system, finding unnamed periodic trajectories in the 3 body system.
1.4 Coupled Oscillator
One pendulum is harmonic. What about two that connect through a string? In this paper, I explore the dynamics of a coupled oscillator as you modify the string lengths.
1.5 ChatGPT Equation Copier
A chrome extension that copies the equation generated on ChatGPT into the equation format on Microsoft Word. It's my first extension published on Chrome Web store, and I'm currently exploring options to market the product.