claudes_game/docs/implementation_plan.md

Orbital Mechanics Simulation - Technical Reference

Overview

3D orbital mechanics simulation using 2-body gravitational model with sphere of influence (SOI) transitions. Built with C-style C++ and raylib.

Technical Constraints

• C-style C++ only: structs and functions, no classes or templates
• RK4 (Runge-Kutta 4th order) integration for physics
• Simple rotations (quaternions deferred)
• raylib for 3D visualization
• Single root body systems only (parent_index = -1 for exactly one body)

Core Data Structures

Vec3 (physics.h)

struct Vec3 {
    double x, y, z;
};

CelestialBody (simulation.h)

struct CelestialBody {
    char name[64];
    double mass;              // kg
    double radius;            // meters
    Vec3 local_position;      // position relative to parent (meters)
    Vec3 local_velocity;      // velocity relative to parent (m/s)
    Vec3 position;            // global position (meters from origin)
    Vec3 velocity;            // global velocity (m/s)
    double soi_radius;        // sphere of influence radius (meters)
    int parent_index;         // index of gravitational parent (-1 for root)
    float color[3];           // RGB for rendering
    double eccentricity;      // orbital eccentricity (0 = circular)
    double semi_major_axis;   // meters
};

SimulationState (simulation.h)

struct SimulationState {
    CelestialBody* bodies;
    int body_count;
    int max_bodies;
    double time;              // simulation time (seconds)
    double dt;                // time step (seconds)
};

RenderState (renderer.h)

struct RenderState {
    Camera3D camera;
    double distance_scale;    // Scale factor for distances
    double size_scale;        // Scale factor for body sizes
    bool show_info;           // Display simulation info
};

OrbitalElements (simulation.h)

struct OrbitalElements {
    double time_days;
    double semi_major_axis_au;
    double eccentricity;
    double specific_energy;
    double distance_to_sun_au;
    double distance_to_ref_body_au;
    double velocity_magnitude;
};

AccelerationContext (physics.h)

struct AccelerationContext {
    SimulationState* sim;
    CelestialBody* current_body;
    int body_index;
};

OrbitalMetrics (test_utilities.h)

struct OrbitalMetrics {
    double kinetic_energy;
    double potential_energy;
    double total_energy;
    double orbital_radius;
    double velocity_magnitude;
    double angular_position;
};

OrbitTracker (test_utilities.h)

struct OrbitTracker {
    double initial_angle;
    double previous_angle;
    int quadrant_transitions;
    bool orbit_completed;
    double time_at_completion;
    int body_index;
    double min_time_days;
};

Module Overview

Physics (physics.cpp/h)

Vector math and gravity calculations. RK4 (Runge-Kutta 4th order) integration with rk4_step(). Physics module is independent of simulation structures and accepts direct parameters for improved modularity.

Key functions:

• rk4_step(Vec3* position, Vec3* velocity, double dt, double body_mass, double parent_mass) - RK4 integration using position/velocity pointers
• evaluate_acceleration(Vec3 relative_pos, double body_mass, double parent_mass) - computes gravitational acceleration from parent

Simulation (simulation.cpp/h)

Simulation state management and updates. SOI detection using Hill sphere: r_soi = a * (m/M)^(2/5).

Key functions:

• find_dominant_body() - determines which body has gravitational dominance
• update_soi() - calculates sphere of influence radius using Hill sphere
• update_simulation() - runs one physics step: finds dominant parent, calculates gravity, applies RK4 integration
• initialize_local_coordinates() - converts global to local coordinates on load
• compute_global_coordinates() - converts local to global coordinates after update
• Dynamic parent switching when bodies cross SOI boundaries (with hysteresis)

Update Order:

• Root bodies updated first (in their own frame = global)
• Global coordinates computed for roots
• Child bodies updated in parent's local frame
• Global coordinates computed for all children

Config Loader (config_loader.cpp/h)

TOML-based config parser using tomlc17 library. Auto-calculates circular orbit velocities and SOI radii.

Key functions:

• parse_toml_body() - parses individual body entries
• calculate_initial_velocities() - sets circular orbit velocities using vis-viva equation
• calculate_soi_radii() - computes sphere of influence for all bodies

Config format details:

• TOML array of tables: [[bodies]]
• Comments start with #
• parent_index = -1 indicates root body (star)
• Supports nested orbits (planets with moons)

Config format (TOML):

[[bodies]]
name = "Sun"
mass = 1.989e30
radius = 6.96e8
position = { x = 0.0, y = 0.0, z = 0.0 }
parent_index = -1
color = { r = 1.0, g = 1.0, b = 0.0 }
eccentricity = 0.0
semi_major_axis = 0.0

[[bodies]]
name = "Earth"
mass = 5.972e24
radius = 6.371e6
position = { x = 1.496e11, y = 0.0, z = 0.0 }
parent_index = 0
color = { r = 0.0, g = 0.5, b = 1.0 }
eccentricity = 0.0
semi_major_axis = 1.496e11

Renderer (renderer.cpp/h)

Raylib 3D visualization with logarithmic distance scaling and size scaling for visibility.

Orbit rendering:

• Elliptical orbits: e < 0.98
• Parabolic orbits: 0.98 ≤ e ≤ 1.02 (uses escape trajectory formula)
• Hyperbolic orbits: e > 1.02 (shows asymptotic behavior)
• render_parabolic_orbit() renders escape paths with true anomaly range: -π0.95 to π0.95

Test Utilities (test_utilities.cpp/h)

Test helper functions for orbital mechanics validation.

Key functions:

• calculate_kinetic_energy() - computes kinetic energy of a body
• calculate_potential_energy_pair() - computes gravitational potential energy between two bodies
• calculate_system_total_energy() - sums total energy of entire system
• calculate_orbital_metrics() - returns comprehensive orbital state metrics
• create_orbit_tracker() - initializes orbit completion tracking
• update_orbit_tracker() - tracks orbital progress and detects completion
• compare_double() / compare_vec3() - floating-point comparison with tolerance

Local Coordinate Frames (simulation.cpp/h)

Hierarchical coordinate system for improved numerical precision in nested orbits.

Key functions:

• initialize_local_coordinates() - initializes local frame positions/velocities from global coordinates
• compute_global_coordinates() - computes global positions/velocities from local frames

Benefits:

• Eliminates large offsets in floating-point calculations (moon at 3.8×10⁸ m instead of 1.5×10¹¹ m)
• Isolates moon orbits from planetary perturbations
• Maintains full floating-point precision for small orbital changes
• Improved Earth-Moon orbital stability (20% drift → stable)

Implementation Details:

• Dual coordinate storage: both local and global coordinates maintained
• Parent bodies treated as origin in child's reference frame during integration
• RK4 integration operates on local coordinates
• Global coordinates computed after each physics step for rendering and SOI checks

Main Program (main.cpp)

GUI-only application with interactive 3D visualization.

• Initializes simulation with MAX_BODIES=100, TIME_STEP=60 seconds
• Runs 100 physics steps per frame (adjustable with speed multiplier)
• Game loop: input handling → camera update → physics update (if not paused) → rendering
• Supports speed multiplier (2x/0.5x per keypress, min 0.125x)
• Default config: tests/configs/solar_system.toml

Controls:

• Arrow keys: Rotate and zoom camera
• Space: Pause/Resume
• +/-: Speed up/slow down simulation
• I: Toggle info display
• ESC: Quit

Build System

Makefile Targets

• make - Build raylib (first time) and compile sources to orbit_sim
• make rebuild - Clean and rebuild
• make clean - Remove build artifacts
• make clean-all - Clean everything including raylib
• make run - Build and run the simulation
• make test - Run full automated test suite
• make test-build - Build test executable

Dependencies

• g++ (C++14)
• raylib (built automatically from ext/raylib/src)
• tomlc17 (included in ext/tomlc17/src)
• Catch2 (for testing)
• libX11, libGL, libpthread (system libraries)

Test Infrastructure

• Framework: Catch2 for unit testing
• Test Configs: tests/configs/ contains test scenarios
  • solar_system.toml - Full solar system with moons
  • earth_circular.toml, mars_circular.toml - Simple orbital tests
  • parabolic_comet.toml - Parabolic orbit (e=1.0)
  • hyperbolic_comet.toml - Hyperbolic orbit (e>1.0)
  • soi_transition.toml - SOI crossing test (3-body system)
• Test Files:
  • test_energy.cpp - Energy conservation validation
  • test_moon_orbits.cpp - Moon orbital stability tests
  • test_orbital_period.cpp - Orbital period verification
  • test_parabolic_orbit.cpp - Parabolic orbit tests
  • test_hyperbolic_orbit.cpp - Hyperbolic orbit tests
  • test_soi_transition.cpp - SOI transition validation

Orbit Types

Elliptical Orbits (0 ≤ e < 1)

• Standard planetary and moon orbits
• Eccentricity e = 0 (circular) to e < 1 (elliptical)
• Total energy is negative (bound to parent)
• Velocity follows vis-viva equation: v² = GM(2/r - 1/a)

Parabolic Orbits (e = 1)

• Escape trajectories with exactly escape velocity
• Total energy is zero (marginally unbound)
• Escape velocity: v² = 2GM/r
• Rendered using true anomaly range: -π0.95 to π0.95
• Used for comets on escape trajectories

Hyperbolic Orbits (e > 1)

• Fast escape trajectories exceeding escape velocity
• Total energy is positive (unbound)
• Asymptotic velocity: v∞ = √(2GM/|a|) where a < 0
• Shows open curve with asymptotic behavior
• Used for high-speed comets and interstellar objects

Data Flow

Initialization Sequence

1. Configuration file → load_system_config() → populates SimulationState
2. calculate_initial_velocities() → sets circular orbit velocities for all bodies
3. calculate_soi_radii() → computes sphere of influence for each body

Main Simulation Loop

1. update_simulation() → for each body:
   • find_dominant_body() → determine gravitational parent based on SOI
   • evaluate_acceleration() → compute gravitational force from parent
   • rk4_step() → update position/velocity using Runge-Kutta 4th order
2. render_simulation() → for each body:
   • scale_position() → convert to render coordinates using logarithmic scaling
   • scale_radius() → convert to render size using exponential scaling
   • render_body() → draw sphere with color

SOI Transition Mechanics

• Bodies dynamically switch gravitational parents when crossing SOI boundaries
• Uses 0.5x distance hysteresis to prevent oscillation between parents
• find_dominant_body() checks all bodies and selects most dominant influence

Implementation Status

✅ Completed

• Phase 1-4: Core physics, simulation, config loading, and rendering
• Raylib integration with 3D camera
• Distance and size scaling for visualization
• TOML config file system with solar system configs (includes Sun + 8 planets + 6 moons)
• RK4 (Runge-Kutta 4th order) integration for improved accuracy
• Time scaling controls (speed up/slow down simulation)
• Pause/resume functionality
• Orbital elements calculation
• Hierarchical coordinate frames (local + global storage)
• Parent-first update order for stability
• Parabolic orbit support (e=1.0)
• Hyperbolic orbit support (e>1.0)
• Physics module refactoring (parameter-based signatures)
• Comprehensive test suite (8 test files, 39+ assertions)
• Build system with automated testing

🔨 Remaining/Future Work

• More accurate integration methods (Newton-Raphson propagation)
• Interactive body selection
• Reference frame switching
• SOI transition frame transformations (Phase 3 of hierarchical frames)
• Io and Titan orbital stability tuning

Technical Notes

Code Style and Architecture

• C-style C++: structs and functions only, no classes or templates
• All headers use include guards
• Memory management uses malloc/free
• Layer separation: Physics, Simulation, Configuration, Rendering layers
• Physics module is independent of simulation structures (parameter-based signatures)

Scaling for Visualization

• Distance: logarithmic/power-law scaling for solar system scale
• Size: minimum visible radius to prevent tiny bodies from disappearing
• Origin at Sun for simplicity
• Both distance_scale and size_scale are configurable in RenderState

Physics Considerations

• Timestep: 60 seconds for solar system scale
• Circular orbit velocity: v = sqrt(G * M / r)
• Physics steps per frame: 100 (default) with speed multiplier adjustment
• Simulation time per frame: 60s * 100 = 6000 seconds at 1x speed
• SOI (Sphere of Influence) uses Hill sphere approximation: r_soi = a * (m/M)^(2/5)
• SOI transitions use 0.5x distance hysteresis to prevent oscillation
• Parabolic orbits use escape velocity: v² = 2GM/r
• Hyperbolic orbits have positive total energy and asymptotic velocity

Future Enhancements

• More accurate integration methods (Newton-Raphson propagation)
• Interactive body selection
• Reference frame switching
• 3D orbital visualization with inclination
• SOI transition frame transformations (Phase 3 of hierarchical frames)