Physics Simulation using Pygame

Welcome to the Simple Physics Engine project! This is a simple physics engine implemented in Python using classical algebra-based physics and the Pygame library. The simulation features circles that interact with each other through gravity and elastic collisions. Below is a brief overview of the project components and how to use the simulation.

Project Structure:

• main.py: The main Python script containing the physics simulation loop and user input handling.
• Circle Class: Defines the Circle class with attributes such as mass, radius, position, and velocity. Handles forces and collisions.
• Collision Functions: Includes functions for elastic collisions, inelastic collisions, and a weighted combination of both.
• Update Physics Function: Updates the physics of each circle based on user input, gravity, and collisions.
• Pygame Setup: Initializes the Pygame window, sets up colors, and defines the main game loop.
• Gravity and Collision Physics: Updates the velocity of circles based on gravitational forces and handles collisions between circles.
• Pygame Drawing: Clears the screen and draws circles with updated positions.

How to Run the Simulation:

1. Make sure you have Python and Pygame installed on your system.
2. Execute the main.py script to launch the simulation.
3. Use the arrow keys to apply forces to the circles and observe their interactions.
4. Close the simulation window to exit.

Circle Class:

The Circle class is a data structure representing individual circles in the simulation. Each circle has its own mass, radius, position, and velocity. The class also includes methods for applying forces and updating its state.

Physics Formulas:

• Gravity: The simulation incorporates a simple gravitational force between circles based on Newton's law of gravitation.
• Collisions: The simulation supports both elastic and inelastic collisions between circles.
  • Perfectly elastic collisions are calculated using formulas that conserve both momentum and kinetic energy.
  • Perfectly inelastic collisions are also supported, where momentum is conserved, but kinetic energy may not be.
  • Partially elastic collisions are also supported, where the elasticity is dependent on a user-defined coefficient of elasticity.

User Input:

• Use the arrow keys to apply forces to the circles. The simulation responds to left, right, up, and down arrow keys.

Customization:

• Adjust the initial setup of circles in the circles list, changing their mass, radius, and initial positions.

Notes:

• The simulation is configured to run at a target frame rate of 60 fps.

Feel free to explore the code, experiment with different parameters, and extend the project according to your preferences. Happy simulating!