Add session summary for hierarchical coordinate frames implementation

Comprehensive summary of Phase 1-2 implementation:
- Multiple root bodies cleanup (-154 lines)
- Phase 1: Dual coordinate storage foundation
- Phase 2: Local frame integration (Earth Moon test passing!)
- Test improvements: 6/9 → 7/9 passing
- Technical details and architecture documentation
- Future work and deferred phases noted

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

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+# 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):**
+```cpp
+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