Comparing Iteration Methods Via Celestial Dynamics

A numerical simulation suite for comparing time-stepping methods by tracing gravitational dynamics of projectiles, two-body systems, and three-body systems. The project is implemented primarily in R, with an optional Python helper for regenerating figure-8 initial conditions.

View the generated results site: https://sidrichardsquantum.github.io/Celestial_Dynamics_Iteration_Methods/

For setup, commands, examples, and repository layout, see USAGE.md. For method descriptions, see THEORY.md. For generated results, evaluation, and comparison dashboards, see RESULTS.md.

Overview

This project compares:

• Euler method
• Midpoint method
• Heun's method
• Runge-Kutta (RK4) method
• Velocity Verlet method

The simulations generate trajectories and energy-conservation diagnostics for:

• projectile motion near Earth's surface
• same-system comparisons across all implemented methods
• Sun-Earth and Earth-Moon two-body systems
• general n-body systems
• special four-body central configurations
• general three-body systems
• special three-body solutions, including figure-8, Lagrange, Euler collinear, and Butterfly I
• restricted three-body examples, including CR3BP and Sitnikov cases

constants.R defines G as positive; attraction is handled by explicit signs in the force equations.

Quick Start

Run all validations:

Rscript tests/run_all_tests.R

Regenerate every example plot:

Rscript run_all_examples.R

Regenerate analysis tables, diagnostics, and the dashboard:

Rscript analysis/generate_results.R

Run only three-body checks:

Rscript tests/validate_three_body.R

Repository Highlights

• iteration_methods/: projectile-oriented method implementations
• celestial_systems/two_body/: two-body solvers, method registry, and shared plotting/physics helpers
• celestial_systems/n_body/: general 2D n-body RK4 and Velocity Verlet engines
• celestial_systems/three_body/: full and restricted three-body helpers
• examples/: runnable examples grouped by model type, including method comparisons
• images/: generated plots grouped by example type
• analysis/: reproducible result-table, diagnostic-plot, and dashboard generation
• tests/: validation scripts used locally and in CI
• .github/workflows/: validation, plot-regeneration, and GitHub Pages deployment workflows

License

This project is licensed under the MIT License. See LICENSE.

Author: Sid Richards (SidRichardsQuantum)