[Python] Pymunk Energy Conservation: Simulating a Bouncing Ball with Perfect Elasticity

Issue with Mechanical Energy Conservation in a Bouncing Ball Simulation (Pymunk)

I'm trying to simulate a simple bouncing ball in Pymunk with perfect elasticity (coefficient of restitution = 1). The ball should conserve mechanical energy, meaning the sum of kinetic and potential energy remains constant over time. However, when I track the total energy of the system, I notice variations instead of a constant value.

The ball has elasticity set to 1. Gravity is applied in the downward direction. No external forces are acting after the initial release.

Despite these conditions, the total energy fluctuates over time. Is there something I'm missing in how Pymunk handles collisions or numerical integration that could explain this issue? How can I ensure better energy conservation in the simulation?

Kinetic Energy: 1551.06, Potential Energy: 405.32, Total Energy: 1956.38 Kinetic Energy: 1569.31, Potential Energy: 395.76, Total Energy: 1965.07

Thank you in advance for your time and help

'''

import pygame
import pymunk
import numpy as np

# Constants
SCREEN_WIDTH = 600
SCREEN_HEIGHT = 400
G = 9.8 # Gravity acceleration

# Initialize Pygame and Pymunk
pygame.init()
screen = pygame.display.set_mode((SCREEN_WIDTH, SCREEN_HEIGHT))
clock = pygame.time.Clock()

# Pymunk Space setup
space = pymunk.Space()
space.gravity = (0, G)

# Ball properties
radius = 30
mass = 1
moment = pymunk.moment_for_circle(mass, 0, radius)

# Create the ball
ball_body = pymunk.Body(mass, moment)
ball_body.position = (SCREEN_WIDTH // 2, SCREEN_HEIGHT // 2)
ball_shape = pymunk.Circle(ball_body, radius)
ball_shape.elasticity = 1.0 # Perfect elasticity
space.add(ball_body, ball_shape)

# Create the floor (static)
floor = pymunk.Segment(space.static_body, (0, SCREEN_HEIGHT - 10), (SCREEN_WIDTH, SCREEN_HEIGHT - 10), 0)
floor.elasticity = 1.0 # Perfect elasticity
space.add(floor)


# Function to calculate energy
def calculate_energy():
# Kinetic energy: 1/2 * m * v^2
velocity = ball_body.velocity
velocity_mag = (velocity[0] ** 2 + velocity[1] ** 2) ** 0.5
kinetic_energy = 0.5 * mass * (velocity_mag ** 2)

# Potential energy: m * g * h
potential_energy = mass * G * (SCREEN_HEIGHT - ball_body.position.y)

# Total energy
total_energy = kinetic_energy + potential_energy
return kinetic_energy, potential_energy, total_energy


# Function to render the ball
def render_ball():
pygame.draw.circle(screen, (255, 0, 0), (int(ball_body.position.x), int(ball_body.position.y)), radius)


# Main loop
running = True
while running:
for event in pygame.event.get():
if event.type == pygame.QUIT:
running = False

# Update the world
space.step(1 / 60)

# Calculate and display energy
kinetic, potential, total = calculate_energy()
print(f"Kinetic Energy: {kinetic:.2f}, Potential Energy: {potential:.2f}, Total Energy: {total:.2f}")

# Clear the screen
screen.fill((255, 255, 255))

# Render the ball
render_ball()

# Update the display
pygame.display.flip()

# Limit FPS
clock.tick(60)

# Quit Pygame
pygame.quit()


'''

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