Coding Projects
I am skilled in coding with Python and have created coding projects to solve problems that I found interesting. For example, I created a simulation of a spin-off of the three-body problem, simulating electromagnetic interactions between charged particles. I also created a program that is able to turn functions into audio. I also know how to code websites.
(The code above is from my Electromagnetic Three-Body Problem Simulation)
Force Simulator
Completed June 2023
Given a force law that is dependent upon position, velocity, both, or neither, it is possible to model the system's time evolution using differential equations. However, it is not always possible to analytically solve the equations. This program uses numerical methods to simulate the position and velocity of the particle over time.
https://github.com/Eashan-Iyer/Force-Simulator
Sample output of the program is below. It is also on GitHub. You will most certainly find it useful to gain an understanding of forces in physics quickly, since the program takes care of all the underlying math, even if there is no analytic solution to the problem.
Trajectory of an object undergoing a simulated linear drag force in 2 dimensions
Velocity vs time plot of an object undergoing a 1-dimensional linear drag force.
Electromagnetic Three-Body Problem Simulation
Completed March 2023
I created a simulation of the three-body problem for fun and decided to create a spin-off that modeled electromagnetic interactions since I was studying those in my AP Physics C class. It simulates the interactions between three point charges. I originally did not put this onto GitHub, since I did not input interesting initial conditions, and got boring graphs where the particles reached an equilibrium where they repelled each other. I found that reducing the simulation time gave less predictable and more interesting results. It is likely that this is because the bodies have a tendency to diverge and travel in different directions, and so by zooming out, the chaotic starting behavior cannot be observed,
https://github.com/Eashan-Iyer/Electromagnetic-3-body-Problem
Sample output of the program is below. It is also on GitHub. Try out different conditions, and see if you can create your own interesting graphs!
Web-Embeddable Calculator
Completed September 2022
I created this calculator for my physics blog. Ultimately, I ended up not using it for the website. However, this is useful for an educational website, since it allows users to interact with the content they learn, and run computations without needing to open a new tab with a calculator. An embed of the calculator is included in this webpage, as well as a link to a GitHub repository containing the code.
Cosmic Cruises
Completed April 2023
For a website development competition (TSA Webmaster), I created a website along with Rishit Arora, Apurva Parasher, and Darsh Shah for a hypothetical space tourism company. Our website placed first in the state of New Jersey in the Technology Student Association Webmaster competition. The team qualified for participating in the 2023 National TSA conference in Louisville, KY. I also wrote a paper about the physics behind our concept and published it on the website.
Audioizer
Completed May 2023
Graphing calculators are programs that visualize functions. Analogously, this program sonifies functions, outputting waveforms with a frequency that evolves with respect to time, based on the function. I was inspired to make this program to create more sensory intuition in mathematics. If you want to use this, you should input an antiderivative of the function that you intend to hear (you can compute that here). I tried to implement this integration directly into the program, but this had a negative impact on how fast it ran. If you know of a solution, I would be very happy to hear it.
Github link
https://github.com/Eashan-Iyer/Audioizer
Sample outputs of the program are on GitHub. I encourage you to experiment!
Analysis of Euler's Method.
Completed January 2023
Given any differential equation, it is possible to approximate the solution over an interval using Euler's method of approximation. This method involves creating lines using the differential equation, extending them out a predetermined delta x value, and then plugging in the endpoint of that line back into the differential equation, then repeating this many times, until the desired value has been approximated. Smaller delta x values will lead to better approximations because they will better respond to changes in the slope that may occur. This method is useful for approximating results for differential equations that are difficult or impossible to solve through techniques such as the separation of variables. Github links are included here. You can find a copy of a write-up that Prathamesh Trivedi and I created on my page for math and physics projects.
https://github.com/Eashan-Iyer/Analysis-of-Eulers-Method