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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 focuses primarily on translational spacecraft dynamics, propulsion force generation, RCS actuator behavior, landing control, and numerical state propagation. Future extensions will introduce rigid-body rotational dynamics, attitude propagation, torque modeling, and more advanced guidance architectures.

The content is divided into several focused topics:

Motion Calculations
Equations of motion, vector-based force aggregation, numerical integration, and spacecraft dynamics
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
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, diagrams, implementation-oriented explanations, 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.