Pendulum Simulation

simple physics | experiment | C | SDL2 | visualization

A simple pendulum experiment written in C using SDL2 for visualization.

This project was made to learn:

• basic physics simulation
• numerical integration (RK4)
• low-level graphics rendering with SDL2

Nothing fancy — just experimenting and learning step by step.

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How It Works (Simple Explanation)

This simulation does not rely on fake movement or animation tricks. Everything is calculated using real physics equations.

🔹 Single Pendulum

A mass swinging under gravity. The motion is stable, smooth, and predictable (simple harmonic motion).

🔹 Double Pendulum

Two connected pendulums. This system is chaotic, meaning:

• extremely sensitive to initial conditions
• small changes produce very different motion
• beautiful and complex trajectories

🔹 RK4 Integrator

Instead of the simple Euler method, this project uses:

Runge-Kutta 4th Order (RK4)

Benefits:

• smoother motion
• better numerical stability
• closer-to-real physics behavior

🔹 Motion Trails

The simulation draws the path of the pendulum over time, allowing you to visualize chaos, symmetry, and patterns.

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Project Structure

pendulum-simulation/
├── src/
│   ├── main.c       # Entry point, SDL initialization & input handling
│   ├── physics.c    # RK4 physics logic (single & double pendulum)
│   ├── physics.h    # Data structures & simulation state
│   ├── render.c     # SDL2 drawing logic & motion trails
│   └── render.h     # Rendering headers
├── Makefile         # Build automation (GCC)
└── README.md        # Project documentation

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Installation

This project requires SDL2 and GCC to be installed on your system.

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Linux (Ubuntu / Debian / WSL)

Install dependencies:

sudo apt update
sudo apt install build-essential libsdl2-dev

Build and run:

make
./pendulum

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Arch Linux / Manjaro

Install dependencies:

sudo pacman -S gcc make sdl2

Build and run:

make
./pendulum

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macOS (Homebrew)

Install Homebrew (if not installed):

/bin/bash -c "$(curl -fsSL https://raw.githubusercontent.com/Homebrew/install/HEAD/install.sh)"

Install dependencies:

brew install sdl2

Build and run:

make
./pendulum

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Windows

Recommended options:

- MSYS2 (recommended)
- MinGW + SDL2
- WSL (Windows Subsystem for Linux)

Using MSYS2:

pacman -S mingw-w64-x86_64-gcc mingw-w64-x86_64-SDL2 make

Then build:

make

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Verify Installation

If the program opens a window and shows a swinging pendulum, your installation is successful.

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Controls

[1]     → Single Pendulum mode
[2]     → Double Pendulum mode (chaotic)
[SPACE] → Pause / Resume simulation
[R]     → Reset simulation
[Scroll]→ Zoom in / Zoom out
[ESC]   → Exit program

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Screenshots

Single Pendulum (Press 1)

Smooth and predictable harmonic motion

Double Pendulum (Press 2)

Chaotic, sensitive, and beautiful motion trails

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📐 Pendulum Physics (The Math)

Variables used in the code:

θ (theta)  : Angle from vertical
ω (omega)  : Angular velocity
L          : Arm length
m          : Mass
g          : Gravity (9.81 m/s²)
dt         : Time step (≈ 0.016 for 60 FPS)

RK4 Formula

NewState = OldState + (dt / 6) × (k1 + 2k2 + 2k3 + k4)

This keeps the simulation stable over long periods of time.

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Why I Made This

- learn numerical physics (RK4)
- practice memory & structure management in C
- experiment with SDL2 rendering

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Fun Fact

This project was inspired after watching the anime:

"Chi: On the Movements of the Earth"
(Chikyuu no Undou ni Tsuite)

It made me realize how beautiful motion can be when described using mathematics.

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📄 License

MIT License — free to use, modify, remix, and experiment.

still learning, still experimenting