Particle Collision Simulation

This repository presents a particle collision simulation using the Leapfrog algorithm to solve the equations of motion. The simulation is implemented with the Pygame library, and the particles interact through elastic collisions.

Features

• Particle movement using the Leapfrog algorithm.
• Vector-based collision handling with velocity and position adjustments.
• Addition of new particles by clicking on the screen.

How it works

1. Leapfrog Algorithm:

   • Updates the positions and velocities of particles using acceleration and intermediate velocities for greater accuracy.
   • Collisions and new trajectories are recalculated using vector algebra.

2. Collisions:

   • Detects collisions between particles based on their distance.
   • Adjusts velocities according to the laws of conservation of momentum and energy for elastic collisions.
   • Prevents overlap by correcting particle positions.

Controls

• Mouse: Left-click to add new particles to the screen.
• ESC key: To exit the simulation.

Code Structure

• Particle: A class representing each particle, containing position, velocity, acceleration, color, and radius attributes.
• check_collision: A function that handles collisions between two particles, adjusting velocities and positions.
• Main Loop: Controls particle movement and drawing on the screen, and detects mouse events.

Requirements

• Python 3.8+
• Pygame 2.0+
• Numpy
• math