claudes_game/docs/session_summaries/2026-01-09-hierarchical-coordinate-frames-phase1-2.md

Session Summary: Hierarchical Coordinate Frames (Phases 1-2)

Date: 2026-01-09 Branch: moon_testing Goal: Implement hierarchical coordinate frames to improve moon orbital stability

Overview

Successfully implemented local coordinate frame integration to improve numerical precision for nested orbits. The Earth-Moon orbital stability test is now passing after switching from global to local frame physics integration.

Changes Made

Phase 0: Cleanup

• Removed multiple root bodies support (barycentric orbit calculations)
• Deleted configs/example_binary_star.toml
• Updated documentation to reflect single-root constraint
• Simplified calculate_initial_velocities() function
• Net: -154 lines

Phase 1: Foundation (Dual Coordinate Storage)

• Added local_position and local_velocity fields to CelestialBody struct
• Implemented initialize_local_coordinates() - converts global→local
• Implemented compute_global_coordinates() - converts local→global
• Updated config loader to initialize local coordinates after velocity calculation
• Updated update_simulation() to maintain coordinate synchronization
• Result: No behavior change, foundation for local frame integration

Phase 2: Local Frame Integration

• Modified rk4_step() to integrate using local coordinates
• Modified evaluate_acceleration() to calculate gravity with parent at origin
• Updated update_simulation() to compute global FROM local (reversed flow)
• Parent bodies treated as origin in child's reference frame
• Result: Earth Moon test NOW PASSING!

Test Results

Before Session:

• Tests passing: 6/9
• Moon failures: 3 (Earth Moon, Io, Titan)

After Phase 1:

• Tests passing: 6/9 (no change, as expected)
• Foundation in place for local frame integration

After Phase 2:

• Tests passing: 7/9 (+16.7% improvement)
• ✅ Earth Moon orbital stability: NOW PASSING (was failing with >20% drift)
• ❌ Io (Jupiter): Still failing (orbit not completing in time)
• ❌ Titan (Saturn): Still failing (NaN drift)

Technical Details

Why Local Frames Work Better

Numerical Precision Issue:

• Moon-Earth distance: ~3.8×10⁸ m
• Earth-Sun distance: ~1.5×10¹¹ m (400x larger!)

Global Frame Problem:

• Moon position: [1.5×10¹¹ + 3.8×10⁸, 0, 0]
• Small orbital changes lost in floating-point precision
• Planetary perturbations on Earth directly affect Moon integration

Local Frame Solution:

• Moon position relative to Earth: [3.8×10⁸, 0, 0]
• Full precision maintained for orbital changes
• Earth's motion isolated from Moon's integration
• Parent at origin simplifies gravity calculation

Implementation Architecture

Data Storage (Dual):

struct CelestialBody {
    Vec3 local_position;   // relative to parent
    Vec3 local_velocity;   // relative to parent
    Vec3 position;         // global (computed)
    Vec3 velocity;         // global (computed)
    // ...
};

Update Flow:

1. Update root bodies (in local frame = global frame)
2. Compute global coordinates for roots
3. Update child bodies (in local frame, parent at origin)
4. Compute global coordinates for children

Key Functions:

• initialize_local_coordinates() - global→local conversion
• compute_global_coordinates() - local→global conversion
• rk4_step() - integrates local coordinates
• evaluate_acceleration() - gravity with parent at origin

Commits

1. a64e1ab - Remove multiple root bodies support from simulation.cpp
2. bc7c646 - Remove binary star config and update documentation
3. 92be7f8 - Phase 1: Add local coordinate frame storage (no behavior change)
4. 052efff - Phase 2: Local frame integration (Earth Moon test now passing!)
5. b1cdbc8 - Update hierarchical_frames_plan.md with Phase 1-2 completion status

Files Modified

Phase 0 (Cleanup):

• src/simulation.cpp (-89 lines)
• configs/example_binary_star.toml (deleted, -63 lines)
• README.md (-3 lines)
• docs/implementation_plan.md (-6 lines, +1 line)

Phase 1:

• src/simulation.h (added local coordinate fields)
• src/simulation.cpp (coordinate conversion functions)
• src/config_loader.cpp (initialization)
• docs/hierarchical_frames_plan.md (created, +326 lines)

Phase 2:

• src/physics.cpp (+15 lines, -7 lines)
• src/simulation.cpp (+2 lines, -1 line)

Documentation:

• docs/hierarchical_frames_plan.md (+110 lines with status update)

Net Changes:

• Cleanup: -158 lines
• Implementation: +336 lines
• Total: +178 lines

Future Work

Deferred (Phase 3-5):

• Phase 3: SOI transition frame transformations (for spacecraft/satellites)
• Phase 4: Full parent-first update order refinement
• Phase 5: Validation suite and optimization

Remaining Test Failures:

• Io and Titan tests may need timestep tuning or stability improvements
• Not critical - core goal achieved (Earth Moon stable)

Ready For:

• Patched conics implementation (after Phase 3)
• Spacecraft/satellite simulation (after Phase 3)
• Further orbital mechanics improvements

Documentation

Created comprehensive implementation plan in docs/hierarchical_frames_plan.md:

• Full architectural design
• Phase-by-phase breakdown
• Technical rationale for design decisions
• Status tracking for all phases
• Notes for future development

Notes

• Single timestep (60s) maintained throughout simulation
• No multi-level hierarchy support (max 2 levels: Sun→Planet→Moon)
• SOI transitions currently work but don't transform coordinates (Phase 3)
• Major success: Local frame integration dramatically improved moon stability
• Clean separation of local/global coordinates enables future enhancements