2D Physics Engine

I wanted to simulate galaxy collisions, didn't really like any physics engines, so I'm making my own now. This is a simple 2d physics engine that uses the Verlet method to calculate position. The goal is that I'll eventually be able to simulate a galaxy collision with it.

Dependencies:

• Install SFML

To compile and run:

Run this to compile (assuming you've SFML on Mac with Homebrew, or just configure a makefile)

g++ -std=c++14 main.cpp -I/opt/homebrew/Cellar/sfml/2.6.1/include -o prog -L/opt/homebrew/Cellar/sfml/2.6.1/lib/ -lsfml-graphics -lsfml-window -lsfml-system

Run with ./prog

Verlet method

The [Verlet method](https://en.wikipedia.org/wiki/Verlet_integration#:~:text=Verlet%20integration%20\(French%20pronunciation%3A%20%5B,dynamics%20simulations%20and%20computer%20graphics.) is a method used to integrate Newton's equations of motion where the velocity is deduced from the last step. My inspiration for using this method and the description below comes from this video and I do not take credit for it.

$$x{n+1} = 2x{n} - x_{n-1} + a_n \Delta t^2$$

Where $x_n$ is the position at step $n$ and $a_n$ is the acceleration at step $n$.

This is similar to Euler's method ($x_{n+1} = x_n + v_n \Delta t$), except that, as stated above, the velocity is deduced from the last step.