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.
