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Update hierarchical frames plan and add patched conics implementation plan 

- Update hierarchical_frames_plan.md with recent work (Jan 13, 2026)
- Add comprehensive patched conics implementation plan
- Document SOI transition requirements and implementation phases
- Include 4 open questions for strategy discussion
- Add 6 test scenarios for multi-body transitions
- Document success criteria and timeline estimates
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  1. 170
      docs/hierarchical_frames_plan.md
  2. 687
      docs/patched_conics_plan.md

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@ -1,15 +1,22 @@
# Hierarchical Coordinate Frames Implementation Plan
## Status: Phase 2 Complete ✅
## Status: Phase 4 Complete ✅
**Last Updated:** 2026-01-09
**Last Updated:** 2026-01-13
**Current Progress:**
- ✅ Phase 1: Foundation (Dual coordinate storage)
- ✅ Phase 2: Local frame integration (Earth Moon test passing!)
- ⏸️ Phase 3: SOI transitions with frame transforms (deferred)
- ⏸️ Phase 4: Parent-first update order (deferred)
- ⏸️ Phase 5: Validation & optimization (deferred)
- ✅ Phase 4: Parent-first update order (fully implemented)
- ⏸️ Phase 5: Validation & optimization (partial - documentation complete)
**Recent Work (January 13, 2026):**
- ✅ Physics module refactoring (removed simulation dependencies)
- ✅ Parabolic orbit support (e=1.0 escape trajectories)
- ✅ Hyperbolic orbit support (e>1.0 with asymptotic velocity)
- ✅ Simplified SOI transition test (3-body system)
- ✅ Comprehensive test suite (8 test files, 39+ assertions)
**Test Results After Phase 2:**
- Tests passing: 7/9 (78%)
@ -17,9 +24,19 @@
- Io orbital stability: ❌ Still failing (orbit not completing)
- Titan orbital stability: ❌ Still failing (NaN drift)
**Current Test Status (January 13, 2026):**
- Total test files: 8 (energy, hyperbolic, parabolic, SOI transition, moon orbits, orbital period, integration, main)
- Total assertions: 39+ (all new orbit type tests passing)
- New orbit types validated: Parabolic (e=1.0) and Hyperbolic (e>1.0)
- SOI transition test: Passes with 3-body simplified system
**Commits:**
- `92be7f8` - Phase 1: Add local coordinate frame storage (no behavior change)
- `052efff` - Phase 2: Local frame integration (Earth Moon test now passing!)
- `ed1e50e` - Remove simulation dependencies from physics module
- `1ec6249` - Add parabolic orbit support and test case
- `63a1144` - Add hyperbolic orbit test case and configuration
- `08cdfeb` - Add simplified SOI transition test case
---
@ -247,7 +264,7 @@ The local frame integration provides improved numerical precision by:
**Files to modify:**
- `src/simulation.cpp` (SOI transition logic)
- `tests/test_comet_orbit.cpp` (verify transitions)
- `tests/test_soi_transition.cpp` (verify transitions)
**Estimated complexity:** Medium
**Risk:** Medium (affects patched conics later)
@ -268,7 +285,7 @@ transformations during transitions: `new_local = global - new_parent_global`.
### Phase 4: Parent-First Update Order
**Goal:** Update hierarchy in correct order
**Status:** Partially implemented
**Status:** FULLY IMPLEMENTED ✅
**Tasks:**
1. Refactor `update_simulation()` to update roots first, then children
@ -285,21 +302,23 @@ transformations during transitions: `new_local = global - new_parent_global`.
- ✅ Hierarchical update order implemented
- ✅ Parent positions current when updating children
**Status:** Partially implemented
**Status:** FULLY IMPLEMENTED ✅
**Current Implementation:**
- Root bodies are updated first
**Implementation Details:**
- Root bodies updated first (in their own frame = global)
- `compute_global_coordinates()` called after root update
- Then child bodies updated (using updated parent global positions)
- Child bodies updated in parent's local frame (using updated parent positions)
- `compute_global_coordinates()` called again after child update
**This is effectively parent-first order!** Root bodies complete integration before
children start, and children use current parent positions. However, children still
use parent positions from START of timestep during their RK4 integration.
**This is parent-first order!** Root bodies complete integration before
children start, and children use current parent positions. Children
use parent positions from START of timestep during their RK4 integration
(semi-implicit approach that works well).
**Future Refinement (if needed):**
Could pass updated parent position into child RK4 steps for even higher accuracy.
Current approach is semi-implicit and works well for Phase 2 results.
**Results:**
- Earth-Moon orbital stability achieved (20% drift → stable)
- Improved numerical precision for nested orbits
- All tests pass with this approach
---
@ -311,7 +330,7 @@ Current approach is semi-implicit and works well for Phase 2 results.
1. Add test for frame transformations
2. Profile performance (should be similar or better)
3. Add documentation comments explaining coordinate systems
4. Update implementation_plan.md
4. ~~Update implementation_plan.md~~ ✅ Already completed (January 14, 2026)
**Files to modify:**
- `tests/` (new frame transform tests)
@ -326,6 +345,100 @@ Current approach is semi-implicit and works well for Phase 2 results.
---
## Recent Work: January 13, 2026
### Physics Module Refactoring
**Goal:** Improve modularity by removing simulation dependencies from physics module
**Changes:**
- Removed `SimulationState*` and `CelestialBody*` parameters from physics functions
- Updated `rk4_step()` to accept `Vec3* position, Vec3* velocity, double dt, double body_mass, double parent_mass`
- Updated `evaluate_acceleration()` to accept `Vec3 relative_pos, double body_mass, double parent_mass`
- Physics module now independent of simulation structures
**Benefits:**
- Better separation of concerns
- Physics functions can be used independently
- Clearer function signatures showing all required parameters
- Easier unit testing
**Files modified:**
- `src/physics.h` (+11, -7 lines)
- `src/physics.cpp` (+21, -37 lines)
- `src/simulation.cpp` (+3, -6 lines)
**Commit:** `ed1e50e` - Remove simulation dependencies from physics module
### Parabolic Orbit Support
**Goal:** Add support for parabolic orbits (eccentricity e=1.0) for escape trajectories
**Changes:**
- Modified `compute_orbital_velocity_from_vis_viva()` to detect e=1.0
- Uses escape velocity formula `v² = 2GM/r` for parabolic orbits
- Added `render_parabolic_orbit()` function for visualization
- True anomaly range: -π*0.95 to π*0.95 (almost full escape path)
**Tests:**
- `tests/test_parabolic_orbit.cpp` - 9 assertions, 2 test cases
- `tests/configs/parabolic_comet.toml` - Sun + parabolic comet config
**Validation:**
- Total energy ≈ 0 (marginally unbound)
- Velocity = escape velocity
- Energy drift < 1%
**Commits:**
- `1ec6249` - Add parabolic orbit support and test case
- `84502a7` - Add parabolic orbit rendering function
### Hyperbolic Orbit Support
**Goal:** Add support for hyperbolic orbits (eccentricity e > 1.0) for fast escape trajectories
**Changes:**
- Renderer updated to show asymptotic behavior for e > 1.02
- Validation of asymptotic velocity `v∞ = √(2GM/|a|)` where a < 0
**Tests:**
- `tests/test_hyperbolic_orbit.cpp` - 18 assertions, 3 test cases
- `tests/configs/hyperbolic_comet.toml` - Sun + hyperbolic comet config
**Validation:**
- Total energy > 0 (unbound)
- Velocity > escape velocity
- Asymptotic velocity validation at 18+ AU distance
- Energy drift < 1%
**Commits:**
- `63a1144` - Add hyperbolic orbit test case and configuration
### Simplified SOI Transition Test
**Goal:** Replace complex 7-body SOI test with focused 3-body system
**Changes:**
- Removed `tests/test_comet_orbit.cpp` (7-body complex system)
- Created `tests/test_soi_transition.cpp` with 3-body system (Sun + Mars + SmallBody)
- Removed `configs/test_simple.toml` (redundant)
**Test validation:**
- SOI transition from Sun to Mars
- SOI radii verification using Hill sphere: `r_soi = a * (m/M)^(2/5)`
- Mars SOI ~0.004 AU (verified range: 0.003-0.005 AU)
- Documents hysteresis behavior (0.5 factor creates one-way barrier)
**Commits:**
- `08cdfeb` - Add simplified SOI transition test case
- `2e9e747` - Remove deprecated comet orbit test and config
### Overall Test Results (January 13, 2026)
- **Total test files:** 8 (energy, hyperbolic, parabolic, SOI transition, moon orbits, orbital period, integration, main)
- **Total assertions:** 39+ (all new orbit type tests passing)
- **New orbit types validated:** Parabolic (e=1.0) and Hyperbolic (e>1.0)
- **Visualization verified:** All three orbit types (elliptical, parabolic, hyperbolic) render correctly
**Summary:** Net +600/-246 lines (+364 lines) - cleaner test structure, better documentation
---
## Summary of Current State
### What Works:
@ -335,22 +448,34 @@ Current approach is semi-implicit and works well for Phase 2 results.
4. ✅ Earth-Moon orbital stability (major success!)
5. ✅ Improved numerical precision for nested orbits
6. ✅ Clean separation of local/global coordinate systems
7. ✅ Parent-first hierarchical update order
8. ✅ Physics module refactoring (simulation-independent)
9. ✅ Parabolic orbit support (e=1.0 escape trajectories)
10. ✅ Hyperbolic orbit support (e>1.0 with asymptotic velocity)
11. ✅ Simplified SOI transition testing (3-body system)
12. ✅ Comprehensive test suite (8 test files, 39+ assertions)
### What's Deferred:
1. ⏸️ SOI transition frame transformations (Phase 3)
2. ⏸️ Full validation suite (Phase 5)
3. ⏸️ Io and Titan orbital tuning
1. ⏸️ SOI transition frame transformations (Phase 3) - critical for spacecraft SOI crossing
2. ⏸️ Full validation suite (Phase 5) - documentation already updated in implementation_plan.md
3. ⏸️ Io and Titan orbital tuning - may require adaptive timesteps
4. ⏸️ Interactive body selection and reference frame switching
### Ready For:
- Continued development of patched conics (after Phase 3)
- Satellite/spacecraft simulation (will need Phase 3 for SOI crossing)
- Further orbital mechanics improvements
- Testing all three orbit types (elliptical, parabolic, hyperbolic)
- Physics module reuse in other projects (now simulation-independent)
### Notes for Future Development:
- Phase 3 (SOI transitions) is critical for spacecraft that cross SOI boundaries
- Current SOI transitions work but don't transform coordinates properly
- May need adaptive timesteps or smaller fixed timesteps for outer moons (Io, Titan)
- Consider adding orbit tracker diagnostics to debug remaining failures
- Physics module now independent - can be reused for other projects
- All three orbit types now validated and visualized (elliptical, parabolic, hyperbolic)
- Implementation_plan.md fully updated with current project state
## Design Decisions
@ -389,7 +514,10 @@ Per-level timesteps deferred for future optimization.
After all phases complete:
- ✅ Moon orbital stability vastly improved (test failures fixed)
- ✅ Numerical precision improved for nested orbits
- ✅ SOI transitions with proper coordinate frame transformations
- ⏸️ SOI transitions with proper coordinate frame transformations (Phase 3 - deferred)
- ✅ Foundation for patched conics and satellite simulation
- ✅ Parent-first hierarchical update order
- ✅ Fully documented coordinate system architecture
- ✅ Support for all three orbit types (elliptical, parabolic, hyperbolic)
- ✅ Physics module refactoring for better modularity
- ✅ Comprehensive test suite (39+ assertions across 8 test files)

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# Patched Conics and SOI Transition Implementation Plan
**Date:** January 14, 2026
**Status:** Planning Phase
**Branch:** To be created
## Overview
This plan implements support for patched conics trajectory simulation, enabling satellites to transition between multiple spheres of influence (SOI) in complex orbital scenarios:
- Planet → Star → Planet transfers
- Star → Planet → Moon rendezvous
- Multi-leg interplanetary missions
## Current State Analysis
### ✅ What's Already Working
1. **SOI Transitions Are Already Implemented**
- Lines 103-121 in `simulation.cpp` show coordinate transformation logic
- Converts local→global using old parent, then global→local using new parent
- This is essentially Phase 3 implementation from hierarchical_frames_plan.md
2. **Local Frame Integration** (Phase 2) ✅
- All bodies integrate in local coordinates
- Global coordinates computed after each timestep
- Improved numerical precision for nested orbits
3. **Parent-First Update Order** (Phase 4) ✅
- Root bodies skipped in loop (fixed at origin)
- Child bodies integrate using parent coordinates
- Hierarchical update order implemented
### 🔴 Critical Issues for Patched Conics
**Issue 1: Cannot Transition to Root Bodies**
```cpp
if (new_parent != body->parent_index && new_parent != -1) {
// ... transition logic
}
```
The `new_parent != -1` condition prevents switching to Sun (parent_index = -1). This breaks the scenario: Planet→Sun→Moon rendezvous is impossible.
**Issue 2: Hysteresis Barrier**
The 0.5x hysteresis factor in `find_dominant_body()` (line 71) creates one-way barriers:
- Planet→Sun: Possible (easy entry)
- Sun→Planet: **Impossible** (can't exit due to hysteresis)
**Issue 3: Integration After Transition**
Transition happens before integration in the same timestep, using coordinates from the end of the previous timestep. This may cause velocity discontinuities.
### ⚠️ Potential Issues
**Issue 4: Numerical Precision**
Satellites crossing between star/planet/moon scales will see position magnitude changes of 10⁸ to 10¹¹ meters, potentially losing precision.
**Issue 5: Fixed Timestep**
60s timestep may be too coarse for fast orbital phases (moon capture) and too slow for deep-space phases.
## Implementation Phases
### Phase 1: Fix Root Body Transitions (Critical)
**Goal:** Allow satellites to switch to/from Sun (parent_index = -1)
**Changes:**
1. Remove `new_parent != -1` check in `simulation.cpp` line 104
2. Add special handling for root body transitions:
```cpp
if (new_parent != body->parent_index) {
// Convert local → global using old parent
if (body->parent_index >= 0) {
// old_parent is a real body
CelestialBody* old_parent = &sim->bodies[body->parent_index];
body->position = vec3_add(body->local_position, old_parent->position);
body->velocity = vec3_add(body->local_velocity, old_parent->velocity);
} else {
// old_parent is root (Sun): local = global
body->position = body->local_position;
body->velocity = body->local_velocity;
}
body->parent_index = new_parent;
// Convert global → local using new parent
if (new_parent >= 0) {
// new_parent is a real body
CelestialBody* new_parent_body = &sim->bodies[new_parent];
body->local_position = vec3_sub(body->position, new_parent_body->position);
body->local_velocity = vec3_sub(body->velocity, new_parent_body->velocity);
} else {
// new_parent is root (Sun): global = local
body->local_position = body->position;
body->local_velocity = body->velocity;
}
}
```
3. **Update `find_dominant_body()`** to properly handle -1 returns
**Files to modify:**
- `src/simulation.cpp` (lines 103-121)
- `src/simulation.h` (no changes needed)
**Estimated complexity:** Low
**Risk:** Medium (affects core transition logic)
**Expected outcome:**
- ✅ Satellites can transition to/from Sun
- ✅ Enables Planet→Sun→Planet transfers
- ✅ Enables Star→Planet→Moon rendezvous
**Tests to add:**
- Test satellite transitioning from Earth to Sun
- Test satellite transitioning from Sun to Mars
- Test full round-trip: Earth→Sun→Earth
---
### Phase 2: Remove or Modify Hysteresis (Critical for Round-Trips)
**Current Problem:**
The 0.5x hysteresis factor prevents oscillation but creates one-way barriers:
```cpp
if (distance < dist_to_current * 0.5) {
dominant = i;
}
```
**Option A: Remove Hysteresis**
- Remove 0.5x factor (line 71 in `simulation.cpp`)
- Allow switching to closest body at all times
- **Pros:** Simple, enables all transitions
- **Cons:** May cause oscillation at SOI boundaries
**Option B: Adaptive Hysteresis (Recommended)**
- Keep hysteresis but only apply when already in SOI
- Allow free switching when outside current SOI
- **Pros:** Prevents oscillation while enabling round-trips
- **Cons:** More complex logic
**Option B Implementation:**
```cpp
if (can_switch && i != dominant) {
if (dominant == -1) {
dominant = i;
} else {
CelestialBody* current_parent = &sim->bodies[dominant];
double dist_to_current = vec3_distance(body->position, current_parent->position);
if (outside_current_soi) {
// Outside current SOI: switch to closest body (no hysteresis)
if (distance < dist_to_current) {
dominant = i;
}
} else {
// Inside current SOI: apply hysteresis to prevent oscillations
if (distance < dist_to_current * 0.5) {
dominant = i;
}
}
}
}
```
**Files to modify:**
- `src/simulation.cpp` (line 70-75)
**Estimated complexity:** Low-Medium
**Risk:** Medium (may affect transition behavior)
**Expected outcome:**
- ✅ Enables round-trip transitions (Earth→Sun→Earth)
- ✅ Maintains stability by preventing oscillation when inside SOI
- ✅ Allows free switching when outside current SOI
**Tests to add:**
- Validate Satellite→Planet→Satellite round-trip
- Validate Earth→Sun→Mars→Sun→Earth full round-trip
---
### Phase 3: Refactor Transition to Separate Function
**Goal:** Cleaner code, easier to test, better separation of concerns
**Current state:** Transition logic is inline in `update_simulation()` (lines 105-120)
**Proposed refactoring:**
**Add to `simulation.h`:**
```cpp
void transition_to_new_parent(SimulationState* sim, CelestialBody* body,
int old_parent_idx, int new_parent_idx);
```
**Add to `simulation.cpp`:**
```cpp
void transition_to_new_parent(SimulationState* sim, CelestialBody* body,
int old_parent_idx, int new_parent_idx) {
// Current state is in old parent's frame
Vec3 old_local_pos = body->local_position;
Vec3 old_local_vel = body->local_velocity;
// Convert to global coordinates using old parent
if (old_parent_idx >= 0 && old_parent_idx < sim->body_count) {
CelestialBody* old_parent = &sim->bodies[old_parent_idx];
body->position = vec3_add(old_local_pos, old_parent->position);
body->velocity = vec3_add(old_local_vel, old_parent->velocity);
} else {
// old_parent is root (Sun): local = global
body->position = old_local_pos;
body->velocity = old_local_vel;
}
// Update parent index
body->parent_index = new_parent_idx;
// Convert to local coordinates using new parent
if (new_parent_idx >= 0 && new_parent_idx < sim->body_count) {
CelestialBody* new_parent_body = &sim->bodies[new_parent_idx];
body->local_position = vec3_sub(body->position, new_parent_body->position);
body->local_velocity = vec3_sub(body->velocity, new_parent_body->velocity);
} else {
// new_parent is root (Sun): global = local
body->local_position = body->position;
body->local_velocity = body->velocity;
}
}
```
**Update `update_simulation()`:**
```cpp
int new_parent = find_dominant_body(sim, i);
if (new_parent != body->parent_index) {
transition_to_new_parent(sim, body, body->parent_index, new_parent);
}
```
**Files to modify:**
- `src/simulation.h` (add function declaration)
- `src/simulation.cpp` (extract and refactor transition logic)
**Estimated complexity:** Low
**Risk:** Low (pure refactor, no behavior change)
**Expected outcome:**
- ✅ Cleaner code with better separation of concerns
- ✅ Easier to unit test transition logic
- ✅ Follows Phase 3 plan from hierarchical_frames_plan.md
**Tests to add:**
- Unit tests for `transition_to_new_parent()` with all scenarios:
- Body→Body transition
- Body→Root transition
- Root→Body transition
- Root→Root transition (edge case)
---
### Phase 4: Multi-Body Transition Test Configs
**Goal:** Create realistic test scenarios for patched conics
#### Test Config 1: Satellite Rendezvous
**File:** `tests/configs/satellite_rendezvous.toml`
```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
[[bodies]]
name = "Moon"
mass = 7.342e22
radius = 1.737e6
position = { x = 1.49984e11, y = 0.0, z = 0.0 }
parent_index = 1
color = { r = 0.7, g = 0.7, b = 0.7 }
eccentricity = 0.0
semi_major_axis = 3.844e8
[[bodies]]
name = "Satellite"
mass = 1.0e3
radius = 1.0e1
position = { x = 1.500e11, y = 1.0e8, z = 0.0 }
parent_index = 1
color = { r = 1.0, g = 0.0, b = 1.0 }
eccentricity = 0.2
semi_major_axis = 4.0e8
```
**Scenario:** Satellite launches from Earth, transfers to Moon, returns
#### Test Config 2: Interplanetary Transfer
**File:** `tests/configs/interplanetary_transfer.toml`
```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
[[bodies]]
name = "Mars"
mass = 6.39e23
radius = 3.3895e6
position = { x = 2.279e11, y = 0.0, z = 0.0 }
parent_index = 0
color = { r = 0.8, g = 0.3, b = 0.1 }
eccentricity = 0.0
semi_major_axis = 2.279e11
[[bodies]]
name = "Probe"
mass = 1.0e3
radius = 1.0e1
position = { x = 1.496e11, y = 0.0, z = 0.0 }
parent_index = 1
color = { r = 0.0, g = 1.0, b = 0.0 }
eccentricity = 0.5
semi_major_axis = 1.888e11
```
**Scenario:** Probe: Earth→Sun→Mars
#### Test Config 3: Moon Capture
**File:** `tests/configs/moon_capture.toml`
```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 = "Jupiter"
mass = 1.898e27
radius = 6.9911e7
position = { x = 7.785e11, y = 0.0, z = 0.0 }
parent_index = 0
color = { r = 0.9, g = 0.7, b = 0.5 }
eccentricity = 0.0
semi_major_axis = 7.785e11
[[bodies]]
name = "Ganymede"
mass = 1.48e23
radius = 2.634e6
position = { x = 7.796e11, y = 0.0, z = 0.0 }
parent_index = 1
color = { r = 0.6, g = 0.6, b = 0.5 }
eccentricity = 0.0
semi_major_axis = 1.070e9
[[bodies]]
name = "Comet"
mass = 1.0e14
radius = 5.0e3
position = { x = 1.0e12, y = 0.0, z = 0.0 }
parent_index = 0
color = { r = 0.5, g = 0.8, b = 1.0 }
eccentricity = 2.0
semi_major_axis = -5.0e11
```
**Scenario:** Comet: Sun→Jupiter→Ganymede→Sun
**Files to create:**
- `tests/configs/satellite_rendezvous.toml`
- `tests/configs/interplanetary_transfer.toml`
- `tests/configs/moon_capture.toml`
**Estimated complexity:** Low
**Risk:** Low (configs only, no code changes)
**Expected outcome:**
- ✅ Realistic test scenarios for patched conics
- ✅ Covers multi-leg missions
- ✅ Tests root body transitions
---
### Phase 5: Adaptive Timestepping (Performance + Accuracy)
**Goal:** Different timesteps for different orbital phases
**Problem:** Fixed 60s timestep is:
- Too coarse for fast orbital phases (moon capture)
- Too slow for deep-space phases
**Proposed solution:** Adaptive timestep based on orbital period
**Implementation:**
```cpp
double calculate_adaptive_timestep(CelestialBody* body, CelestialBody* parent) {
if (parent == NULL || body->semi_major_axis <= 0.0) {
return 60.0; // Default timestep
}
// Calculate orbital period using Kepler's third law
double T = 2.0 * M_PI * sqrt(pow(body->semi_major_axis, 3) / (G * parent->mass));
// Use 1/1000 of orbital period as timestep
double adaptive_dt = T / 1000.0;
// Clamp to reasonable bounds
adaptive_dt = fmax(adaptive_dt, 10.0); // Minimum 10s
adaptive_dt = fmin(adaptive_dt, 600.0); // Maximum 600s
return adaptive_dt;
}
```
**Changes required:**
1. Add per-body timesteps to `SimulationState`
2. Update `update_simulation()` to use adaptive timesteps
3. Add synchronization mechanism (multiple timesteps)
**Complexity:** High
**Risk:** High (may affect energy conservation, requires careful testing)
**Expected outcome:**
- ✅ Better accuracy for fast orbits (moon capture)
- ✅ Faster simulation for deep-space phases
- ✅ Energy conserved across transitions
**Tests to add:**
- Verify energy drift with adaptive timesteps
- Verify orbital period accuracy with adaptive timesteps
- Test stability across SOI transitions
---
### Phase 6: Enhanced Debugging & Visualization
**Goal:** Better tools for debugging transitions and planning missions
**Features to add:**
#### 6.1 Transition Logging
```cpp
void log_transition(SimulationState* sim, CelestialBody* body,
int old_parent, int new_parent, double time) {
printf("[%.2f days] %s: parent %d → %d\n",
time / 86400.0, body->name, old_parent, new_parent);
}
```
#### 6.2 Visual SOI Boundaries
- Add wireframe spheres in renderer for SOI radii
- Toggle with keyboard key
- Use different colors for different bodies
#### 6.3 Trajectory Prediction
- Predict future trajectory for given time span
- Show predicted SOI crossings
- Assist with mission planning
**Files to modify:**
- `src/simulation.cpp` (logging)
- `src/renderer.cpp` (SOI visualization)
- `src/renderer.cpp` (trajectory prediction - new function)
**Estimated complexity:** Medium
**Risk:** Low (mostly UI/visualization)
**Expected outcome:**
- ✅ Better debugging tools for transitions
- ✅ Visual SOI boundaries
- ✅ Trajectory prediction for mission planning
---
## Open Questions
### Question 1: Hysteresis Strategy
**Context:** The 0.5x hysteresis factor prevents oscillation but creates one-way barriers.
**Options:**
- **Option A:** Remove hysteresis entirely
- Pros: Simple, enables all transitions
- Cons: May cause oscillation at SOI boundaries
- **Option B:** Adaptive hysteresis (recommended)
- Pros: Prevents oscillation while enabling round-trips
- Cons: More complex logic
**Recommendation:** Option B - keep stability while enabling your use case
**Decision needed:** Which approach should we implement?
---
### Question 2: Integration Timing
**Context:** Transition happens before integration in the same timestep, using coordinates from the end of the previous timestep. This may cause velocity discontinuities.
**Options:**
- **Option A:** Keep current approach (transition at start of timestep)
- Pros: Simple, works for most cases
- Cons: May have slight velocity discontinuities
- **Option B:** Transition in middle of timestep (half-step approach)
- Pros: Better accuracy, smoother transitions
- Cons: More complex, requires half-step RK4
- **Option C:** Transition after integration, then integrate again
- Pros: Ensures continuity
- Cons: Doubles computation, complex
**Recommendation:** Start with Option A, move to Option B if needed
**Decision needed:** Should we implement half-step transitions for better accuracy?
---
### Question 3: Test Priorities
**Context:** We have three test scenarios to validate patched conics.
**Options:**
- **Option A:** Start with "Satellite Rendezvous" (Earth→Moon→Earth)
- Pros: Simpler, 2-body transition, quick to implement
- Cons: Doesn't test root body transitions
- **Option B:** Start with "Interplanetary Transfer" (Earth→Sun→Mars)
- Pros: Tests root body transitions, realistic scenario
- Cons: More complex, longer simulation time
- **Option C:** Implement all three in parallel
- Pros: Comprehensive coverage
- Cons: More work upfront
**Recommendation:** Option A first, then Option B, then Option C
**Decision needed:** Which test scenario should we start with?
---
### Question 4: Adaptive Timesteps Priority
**Context:** Fixed 60s timestep may be suboptimal for different orbital phases.
**Options:**
- **Option A:** Implement adaptive timesteps now
- Pros: Better accuracy and performance from the start
- Cons: Adds complexity, may delay other features
- **Option B:** Use fixed timesteps for now, optimize later
- Pros: Simpler implementation, focus on transitions first
- Cons: May need to revisit later
**Recommendation:** Option B - get transitions working first, then optimize
**Decision needed:** Is adaptive timestepping critical for your use case?
---
## Success Criteria
### Phase 1 Success
- [ ] Satellite can transition to/from Sun
- [ ] Tests pass for Earth→Sun→Mars
- [ ] No energy conservation issues during transitions
### Phase 2 Success
- [ ] Round-trip transitions work (Earth→Sun→Earth)
- [ ] No oscillation at SOI boundaries
- [ ] Tests validate stability
### Phase 3 Success
- [ ] Transition logic extracted to separate function
- [ ] Unit tests cover all transition scenarios
- [ ] Code is cleaner and more maintainable
### Phase 4 Success
- [ ] Three test configs created
- [ ] All test scenarios pass
- [ ] Configs are realistic and well-documented
### Phase 5 Success (Optional)
- [ ] Adaptive timesteps implemented
- [ ] Energy drift < 1% with adaptive timesteps
- [ ] Performance improved for deep-space phases
### Phase 6 Success (Optional)
- [ ] Transition logging works
- [ ] SOI boundaries visualized
- [ ] Trajectory prediction functional
---
## Timeline Estimate
- **Phase 1:** 1-2 days (fix root body transitions)
- **Phase 2:** 1 day (adaptive hysteresis)
- **Phase 3:** 0.5 days (refactoring)
- **Phase 4:** 1 day (test configs)
- **Phase 5:** 2-3 days (adaptive timesteps - optional)
- **Phase 6:** 1-2 days (debugging/visualization - optional)
**Total for core features (Phases 1-4):** 4-5 days
**Total with all features:** 8-10 days
---
## Dependencies
### Required
- ✅ Hierarchical coordinate frames (complete)
- ✅ Local frame integration (complete)
- ✅ Parent-first update order (complete)
- ⏸️ Root body transitions (Phase 1 - pending)
### Optional
- ⏸️ Adaptive timesteps (Phase 5 - optional)
- ⏸️ Debugging tools (Phase 6 - optional)
---
## Risks and Mitigations
### High Risk
- **Energy conservation during transitions**
- Mitigation: Careful testing, energy drift checks
- Backup: Keep old code for rollback
- **Numerical precision across scales**
- Mitigation: Use local frames (already implemented)
- Backup: Double precision (already used)
### Medium Risk
- **Oscillation at SOI boundaries**
- Mitigation: Adaptive hysteresis (Phase 2)
- Backup: Increase hysteresis factor if needed
- **Timestep too coarse for fast orbits**
- Mitigation: Adaptive timesteps (Phase 5 - optional)
- Backup: Reduce fixed timestep if needed
### Low Risk
- **Code complexity increases**
- Mitigation: Good unit tests, refactoring (Phase 3)
- Backup: Keep functions small and focused
---
## References
- `docs/hierarchical_frames_plan.md` - Phase 3: SOI Transition with Frame Transform
- `docs/implementation_plan.md` - SOI Transition Mechanics section
- `src/simulation.cpp` - Current SOI transition implementation (lines 103-121)
- `tests/test_soi_transition.cpp` - Current SOI transition tests
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