Skip to main content

Mathematics of Spaceflight Dynamics Framework

This section provides an overview of the mathematical models and engineering formulations used throughout the Spaceflight Dynamics Framework (SDF).

The framework is developed as a research-oriented simulation environment focused on spacecraft dynamics, propulsion modeling, guidance and control, telemetry generation, and future 6DOF spacecraft state propagation.

The current mathematical scope covers translational and rotational spacecraft dynamics, quaternion attitude propagation, propulsion and RCS actuator behavior, control allocation, closed-loop attitude stabilization, landing control, coordinate transformations, and numerical state propagation.

The content is divided into several focused topics:

Motion Calculations
Equations of motion, vector-based force aggregation, numerical integration, and spacecraft dynamics
Rotational Dynamics
Rigid-body rotation, torque and attitude propagation
Thrust Model
Main engine thrust generation, response dynamics, fuel consumption, and propulsion force modeling
Reaction Control System
Binary thruster dynamics, actuator delay, first-order response behavior, and RCS propulsion modeling
RCS Control Allocation
Geometry-based allocation of translational and rotational RCS commands to individual spacecraft thrusters
Quaternion Attitude Controller
Quaternion attitude error, angular-rate damping, attitude hold, and hysteresis for discrete RCS stabilization
Impact & Structural Integrity
Landing loads, impact velocity evaluation, crash conditions, and integrity assessment
Adaptive Descent Controller
Energy-based guidance, brake-ratio logic, adaptive control behavior, and descent stabilization
Coordinate Frames & Transformation
Coordinates used and coordinate transformations

Each subpage contains equations, model assumptions, diagrams, verification results, and engineering rationale for the corresponding simulation subsystem.

The mathematical documentation is intended not only as reference material for the current implementation, but also as part of the long-term transition toward a reusable and extensible spacecraft dynamics research framework.