Celestial_Dynamics_Iteration_Methods/index.html at main · SidRichardsQuantum/Celestial_Dynamics_Iteration_Methods · GitHub

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<!doctype html>
<html lang="en">
  <head>
    <meta charset="utf-8">
    <meta name="viewport" content="width=device-width, initial-scale=1">
    <meta
      name="description"
      content="Celestial Dynamics Iteration Methods is an R numerical simulation suite comparing Euler, Midpoint, Heun, RK4, and Verlet methods across projectile, two-body, and three-body gravitational systems."
    >
    <meta name="theme-color" content="#0f5364">
    <title>Celestial Dynamics | Iteration Methods Comparison</title>
    <link rel="stylesheet" href="styles.css">
  </head>
  <body>
    <a class="skip-link" href="#top">Skip to main content</a>
    <header class="site-header">
      <a class="brand" href="#top" aria-label="Celestial Dynamics home">
        <span class="brand-mark">SR</span>
        <span>Celestial Dynamics</span>
      </a>
      <nav class="nav-links" aria-label="Primary navigation">
        <a href="#methods">Methods</a>
        <a href="#systems">Systems</a>
        <a href="#results">Results</a>
        <a href="#package">Package</a>
      </nav>
    </header>

    <main id="top" tabindex="-1">
      <section class="hero section">
        <div class="hero-copy">
          <p class="eyebrow">Numerical methods and orbital simulation</p>
          <h1>Celestial Dynamics Iteration Methods</h1>
          <p class="hero-text">
            A numerical simulation suite comparing Euler, Midpoint, Heun, RK4,
            and Velocity Verlet methods across projectile motion, two-body
            orbits, and three-body gravitational systems.
          </p>
          <div class="hero-actions">
            <a class="button primary" href="analysis/generated/index.html">Generated Results</a>
            <a class="button" href="https://github.com/SidRichardsQuantum/Celestial_Dynamics_Iteration_Methods" target="_blank" rel="noopener noreferrer">GitHub Repo</a>
            <a class="button" href="https://sidrichardsquantum.r-universe.dev/CelestialDynamicsIterationMethods" target="_blank" rel="noopener noreferrer">R-universe</a>
            <a class="button" href="https://sidrichardsquantum.github.io/" target="_blank" rel="noopener noreferrer">Main Portfolio</a>
          </div>
        </div>

        <div class="hero-side">
          <figure class="hero-visual">
            <img
              src="images/comparisons/sun_earth_all_methods.png"
              alt="Sun-Earth orbit comparison generated by multiple numerical integration methods"
            >
          </figure>
          <aside class="focus-panel" aria-label="Project focus areas">
            <h2>Project Focus</h2>
            <ul>
              <li>Compare first, second, fourth, and symplectic time-stepping methods.</li>
              <li>Measure trajectory error, energy drift, and angular momentum conservation.</li>
              <li>Generate reproducible figures, CSV diagnostics, and interactive HTML results.</li>
              <li>Package the simulation helpers for R workflows and R-universe installation.</li>
            </ul>
          </aside>
        </div>
      </section>

      <section id="methods" class="section">
        <div class="section-heading">
          <p class="eyebrow">Implemented solvers</p>
          <h2>Five iteration methods under the same gravitational tests</h2>
          <p>
            The suite keeps the problem setup fixed while swapping the integration
            rule, making long-horizon stability and conservation behavior easy to
            compare.
          </p>
        </div>

        <div class="project-grid method-grid">
          <article class="project-card">
            <div>
              <h3>Euler</h3>
              <p>
                A first-order baseline that makes accumulated position and energy
                error visible in orbital problems.
              </p>
            </div>
            <div class="tags">
              <span>First order</span>
              <span>Explicit</span>
              <span>Baseline</span>
            </div>
          </article>

          <article class="project-card">
            <div>
              <h3>Midpoint</h3>
              <p>
                A second-order Runge-Kutta method that improves local accuracy with
                a half-step slope estimate.
              </p>
            </div>
            <div class="tags">
              <span>Second order</span>
              <span>RK2</span>
              <span>Trajectory error</span>
            </div>
          </article>

          <article class="project-card">
            <div>
              <h3>Heun</h3>
              <p>
                A predictor-corrector method that averages initial and corrected
                slopes for second-order convergence.
              </p>
            </div>
            <div class="tags">
              <span>Second order</span>
              <span>Predictor-corrector</span>
              <span>Convergence</span>
            </div>
          </article>

          <article class="project-card">
            <div>
              <h3>RK4</h3>
              <p>
                A fourth-order reference method used for high-accuracy trajectories
                and convergence comparisons.
              </p>
            </div>
            <div class="tags">
              <span>Fourth order</span>
              <span>Reference</span>
              <span>Accuracy</span>
            </div>
          </article>

          <article class="project-card">
            <div>
              <h3>Velocity Verlet</h3>
              <p>
                A symplectic method included for its strong qualitative behavior in
                conservative orbital systems.
              </p>
            </div>
            <div class="tags">
              <span>Symplectic</span>
              <span>Energy behavior</span>
              <span>Orbital dynamics</span>
            </div>
          </article>
        </div>
      </section>

      <section id="systems" class="section split-section">
        <div class="section-heading">
          <p class="eyebrow">Simulation domains</p>
          <h2>Projectile, two-body, three-body, and n-body examples</h2>
          <p>
            The examples start with simple trajectories and scale up to special
            three-body solutions, restricted three-body cases, and multi-body
            conservation checks.
          </p>
        </div>
        <div class="system-list">
          <article class="system-row">
            <span class="system-index">01</span>
            <div>
              <h3>Projectile Motion</h3>
              <p>Near-surface trajectory examples for method behavior in a compact setup.</p>
            </div>
          </article>
          <article class="system-row">
            <span class="system-index">02</span>
            <div>
              <h3>Two-Body Orbits</h3>
              <p>Sun-Earth and Earth-Moon systems with energy and angular momentum diagnostics.</p>
            </div>
          </article>
          <article class="system-row">
            <span class="system-index">03</span>
            <div>
              <h3>Three-Body Systems</h3>
              <p>General, restricted, and special solutions including figure-8 and Lagrange cases.</p>
            </div>
          </article>
          <article class="system-row">
            <span class="system-index">04</span>
            <div>
              <h3>N-Body Conservation</h3>
              <p>Multi-body validation cases for long-run energy and angular momentum drift.</p>
            </div>
          </article>
        </div>
      </section>

      <section id="results" class="section">
        <div class="section-heading">
          <p class="eyebrow">Generated analysis</p>
          <h2>Results remain available as the full reproducible analysis site</h2>
          <p>
            The generated output is preserved under <code>analysis/generated/</code>,
            including the narrative results page, dashboard, artifact browser, CSV
            summaries, documentation, and example views.
          </p>
        </div>

        <div class="feature-grid">
          <article class="feature-card">
            <img
              src="images/analysis/convergence_rates.png"
              alt="Convergence rate plot for the implemented numerical methods"
            >
            <div>
              <h3>Convergence and Accuracy</h3>
              <p>
                Compare observed order, final position error, and runtime behavior
                against a fine RK4 reference.
              </p>
            </div>
            <div class="card-links">
              <a href="analysis/generated/method_comparison_dashboard.html">Method Dashboard</a>
            </div>
          </article>

          <article class="feature-card">
            <img
              src="images/three_body/special_solutions/three_earths.png"
              alt="Figure-8 three-body choreography generated by the simulation suite"
            >
            <div>
              <h3>Orbital Examples</h3>
              <p>
                Inspect generated two-body, three-body, restricted three-body, and
                n-body plots alongside their source artifacts.
              </p>
            </div>
            <div class="card-links">
              <a href="analysis/generated/artifact_index.html">Artifact Browser</a>
            </div>
          </article>
        </div>
      </section>

      <section id="package" class="section contact-section">
        <div>
          <p class="eyebrow">Package and source</p>
          <h2>Install, inspect, or continue into the generated report</h2>
          <p>
            The project is implemented primarily in R, with static Pages output
            generated from the solver code and analysis scripts.
          </p>
        </div>
        <div class="contact-actions">
          <a class="button primary" href="analysis/generated/index.html">Generated Results</a>
          <a class="button" href="https://sidrichardsquantum.r-universe.dev/CelestialDynamicsIterationMethods" target="_blank" rel="noopener noreferrer">R-universe</a>
          <a class="button" href="https://github.com/SidRichardsQuantum/Celestial_Dynamics_Iteration_Methods" target="_blank" rel="noopener noreferrer">GitHub Repo</a>
          <a class="button" href="https://sidrichardsquantum.github.io/" target="_blank" rel="noopener noreferrer">Main Portfolio</a>
        </div>
      </section>
    </main>

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