ΑETHERION — Flight Dynamics Library

AETHERION is a high-precision, research-grade C++ library for rocket and aerospace flight dynamics, built on:

• Featherstone 6-D Spatial Vector Algebra (SVA)
• ECI / WGS84 frame transformations
• Algorithmic Differentiation (AD-friendly)
• Clean ODE formulations for high-fidelity simulation

The name ΑΙΘΕΡΙΟΝ (Aetherion) is inspired by the Greek word Αιθήρ, referring to the upper atmosphere — the pristine realm of celestial motion.

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Two-Stage Rocket to Orbit — NASA Validation

The flagship simulation is a full 6-DOF two-stage rocket gravity-turn ascent from the equator, validated against NASA TM-2015-218675 Atmospheric Scenario 17. The trajectory below was produced entirely by Aetherion using Featherstone SVA dynamics, the US1976 atmosphere, WGS84 gravity, and an implicit RADAU-IIA integrator.

Stage separation, coast phases, and second-stage ignition are all captured with sub-percent error versus the NASA reference. Final altitude error: 0.87 % · Final speed error: 0.001 %.

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Features

Dynamics Core

• Full 6-DOF rigid-body dynamics using Featherstone Spatial Vector Algebra
• ECI equations of motion — no pseudo-forces, no approximations
• Air-relative velocity for aerodynamics; rotating atmosphere handled correctly
• Variable-mass bodies — propellant burn, staging events, CG travel

Numerical Methods

• Lie-structure-preserving Runge-Kutta-Munthe-Kaas (RKMK) integrator on SE(3)
• Fully implicit RADAU-IIA solver for stiff ascent phases
• Discrete Extended Kalman Filter on a product manifold containing Lie groups

Algorithmic Differentiation

• AD-friendly formulations throughout — compatible with CppAD, dual numbers, and similar libraries
• Auto-Jacobians fed directly into the EKF/UKF linearisation pipeline

Environment Models

• US1976 Standard Atmosphere (temperature, pressure, density, speed of sound)
• WGS84 gravity model with ECI/ECEF/geodetic coordinate conversions
• Branch-free formulations designed for AD and Kalman filtering

Aerodynamics & Propulsion

• DAVE-ML (DML) aerodynamic model loader — table-driven aero/inertia/propulsion data
• Multi-axis force and moment models; CG-offset spatial inertia
• Stage-aware propellant tracking with automatic separation logic

Interoperability

• FMI/FMU export via fmu4cpp — drop Aetherion plants into any FMI-compliant simulator
• JSON configuration files for initial conditions and simulation parameters
• CSV output compatible with NASA reference data formats

Code Quality

• Post-modern C++23 design throughout
• Enforces a practical subset of the JSF AV C++ coding standard
• CI gates: Clang-Format · CMake-Format · CMake-Lint · IWYU · Clang-Tidy · Metrix++ cyclomatic complexity · AddressSanitizer / UBSan

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SVA → AD → EKF Pipeline

The library is architected so that the same smooth ẋ = f(x, u) used for simulation feeds auto-Jacobians into the EKF linearisation, producing a single consistent GNC pipeline from plant model to state estimator.

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Mathematical Foundations

ΑETHERION implements the full suite of Featherstone spatial constructs:

Symbol	Meaning
v	Spatial velocity (twist)
a	Spatial acceleration
I	Spatial inertia
v×	Motion cross-product operator
v×*	Force cross-product operator (adjoint)

Equation of motion:

Control surfaces and payload stages can be modelled as rigidly attached bodies within the same spatial algebra.

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Frames & Conventions

Label	Frame
W	Inertial (ECI)
E	Earth-fixed (ECEF)
B	Rocket/aircraft body

All transforms follow:

notation for spatial transforms, keeping the frame algebra explicit and AD-friendly.

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Validated Examples

Example	Vehicle	Reference
TwoStageRocket	Two-stage launch vehicle	NASA TM-2015-218675 Scenario 17
F16SteadyFlight	F-16 at trim	NASA TN D-8532 Section 13.1
F16AirspeedChange	F-16 speed step	NASA TN D-8532 Section 13.2
F16AltitudeChange	F-16 altitude step	NASA TN D-8532 Section 13.3
F16HeadingChange	F-16 heading change	NASA TN D-8532 Section 13.4
F16LateralSideStep	F-16 lateral manoeuvre	NASA TN D-8532 Appendix
F16SupersonicTrim	F-16 supersonic trim	NASA TN D-8532
EastwardCannonball	Point mass projectile	Analytic (Coriolis)
NorthwardCannonball	Point mass projectile	Analytic (Coriolis)
SphereWithAtmosphericDrag	Sphere + drag	Analytical reference
DroppedSphereSteadyWind	Sphere in steady crosswind	Analytical reference
DroppedSphere2DWindShear	Sphere in wind-shear field	Analytical reference
TumblingBrickNoDamping	Free tumbling rigid body	Angular momentum conservation
TumblingBrickWithDamping	Damped tumbling body	Energy dissipation
CircleEquatorDateLine	Orbital-like equatorial loop	Geometric consistency
CircleNorthPole	Polar orbital loop	Geometric consistency

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Testing

• Catch2 unit tests covering every module
• Numerical validation against NASA technical reports (sub-percent agreement)
• AddressSanitizer + UBSanitizer run on every CI push
• Clang-Tidy static analysis and IWYU include hygiene enforced on every PR

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Dependencies

Library	Purpose
Eigen	Linear algebra
CppAD	Algorithmic differentiation
fmu4cpp	FMI/FMU export
ecos	FMI co-simulation engine (FMU smoke testing)
Catch2 v3	Unit testing

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Documentation

Full API reference and simulation guides are hosted on GitHub Pages:

• Detailed Documentation

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Build & Installation

Clone the repository and initialise submodules:

git clone https://github.com/onurtuncer/Aetherion.git
cd Aetherion
git submodule update --init --recursive

Windows — Visual Studio

1. Open Visual Studio
2. File → Open Folder… → select the Aetherion directory
3. Let Visual Studio configure CMake automatically
4. Choose a configuration (e.g. x64-Release)
5. Build → Build All

Linux / macOS — CMake

cmake -B build -DCMAKE_BUILD_TYPE=Release
cmake --build build --parallel
ctest --test-dir build

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Community

• Bug Tracker: GitHub Issues
• Discussions: GitHub Discussions

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Author

Prof. Dr. Onur Tuncer
Aerospace Engineer, Researcher & C++ Systems Developer
Istanbul Technical University · onur.tuncer@itu.edu.tr