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.

Website: https://sidrichardsquantum.github.io/Celestial_Dynamics_Iteration_Methods/

R-universe: https://sidrichardsquantum.r-universe.dev/CelestialDynamicsIterationMethods

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

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

Installation

Install the development package directly from GitHub:

install.packages("remotes")
remotes::install_github("SidRichardsQuantum/Celestial_Dynamics_Iteration_Methods")

After R-universe has built the package, install from R-universe:

options(repos = c(
  sidrichardsquantum = "https://sidrichardsquantum.r-universe.dev",
  CRAN = "https://cloud.r-project.org"
))
install.packages("CelestialDynamicsIterationMethods")

R-universe setup notes and the registry details are in docs/R_UNIVERSE.md.

Common Commands

Run the validation suite:

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

For source checkouts, example-specific commands, optional Python setup, and generated artifact details, see docs/USAGE.md.

Documentation

• Usage: setup, commands, examples, repository layout, and generated artifacts
• Theory: method descriptions and numerical context
• Results: generated results, evaluation, and comparison dashboards
• R-universe setup: package registry and install details

Repository Highlights

• DESCRIPTION and NAMESPACE: lightweight R package metadata
• R/load.R: project-root-aware loading helpers used by scripts and tests
• R/methods/: projectile-oriented method implementations
• R/systems/two_body/: two-body solvers, method registry, and shared plotting/physics helpers
• R/systems/n_body/: general 2D n-body RK4 and Velocity Verlet engines
• R/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
• docs/: usage, theory, and canonical results narrative
• 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)