🎯 2D Particle Collision Simulator 💥

A 2D physics simulator that models elastic and inelastic collisions between multiple particles with real-time visualization. Perfect for demonstrating fundamental physics principles and computational physics implementations.

Elastic Collision:

Totally Inelastic Collision of 3 Particles at an Angle:

✨ Features

• Dual Collision Models
  👉 Full support for both perfectly elastic and inelastic collisions
• Multi-Particle System
  👉 Simulate any number of particles with customizable properties
• Real-time Visualization
  👉 Built with Pygame for smooth graphical representation
• Physics-Accurate
  👉 Implements conservation of momentum and kinetic energy principles
• Customizable Parameters
  👉 Adjust mass, velocity, restitution coefficients, and more
• Optimized Performance
  👉 Efficient collision detection algorithms for smooth operation

Installation ⚙️

1. Clone the repository

git clone https://github.com/SulkBash/Collision-Simulator.git
cd Collision-Simulator

2. Install dependencies

cd Collision_Sim
pip install -r requirements.txt

3. Run the simulation

python collision.py

🔬 Technical Implementation

Physics Foundations

The force is only applied perpendicular to the plane of collision, so the tangential velocity remains unchanged (no force = no acceleration)

1. Conservation of Momentum and Impulse

$$m_1\vec{v}_1 + m_2\vec{v}_2 = m_1\vec{v}_1' + m_2\vec{v}_2'$$

The unit vector in the normal direction of the collision is:

$$\hat{n} = \dfrac{\vec{r_2}-\vec{r_1}}{||\vec{r_2}-\vec{r_1}||}$$

Where r1 and r2 are the position vectors of each particle. Then, by the Impulse-Momentum theorem:

$$J = J_1 = - J_2 = \lambda \hat{n}$$ $$\Rightarrow \vec{p'_1} - \vec{p_1} = J_1 = \lambda \hat{n}$$ $$\vec{p'_2} - \vec{p_2} = J_2 = -\lambda \hat{n}$$

2. Coefficient of Restitution

$$e = \dfrac{v'_{1n}-v'_{2n}}{v_{1n}-v_{2n}}$$

Combining all these equations one can solve for the:

3. Equations of Final Velocities

$$\vec{v'_1} = \vec{v_1} + \dfrac{m_2}{m_1+m_2}(e+1)((\vec{v_2}-\vec{v_1})\cdot \hat{n})\hat{n}$$ $$\vec{v'_2} = \vec{v_2} - \dfrac{m_1}{m_1+m_2}(e+1)((\vec{v_2}-\vec{v_1})\cdot \hat{n})\hat{n}$$

Please observe that when e = 1 (elastic collision), you arrive at the well known equations for the final velocites after an elastic collision

Dependencies 📦

• Python 3.8+
• Pygame
• NumPy

Contributions are Welcome! 🤝

1. Fork the Repository
2. Create your feature branch (git checkout -b feature/amazing-feature)
3. Commit your changes (git commit -m 'Add some amazing feature')
4. Push to the branch (git push origin feature/amazing-feature)
5. Open a Pull Request

📜 License

Distributed under the MIT License. See for more information.