Problem Bank
This section presents engineering-style worked problems in spacecraft dynamics, orbital mechanics, and guidance–navigation–control systems.
Each problem is structured to connect: problem context → model → solution → code → engineering insight.
Designing a Hohmann Transfer: Beyond the Equation
This worked example develops the classical two-impulse Hohmann transfer as a complete engineering walkthrough — connecting assumptions, mathematical modeling, step-by-step solution, and Python implementation.
The problem includes both symbolic formulation and practical cases, including a LEO orbit raise and an Earth parking orbit to GEO transfer.
- What assumptions make the Hohmann transfer Δv-optimal?
- How do the two burns change orbital energy?
- Why is a GEO transfer significantly more expensive than a small orbit raise?
- How can the full calculation be implemented cleanly in Python?
This worked problem connects:
problem context → assumptions → model → solution → code → engineering insightFixing a Spacecraft GNC Model: From Broken Dynamics to Stable Control
This interactive lab turns a simplified spacecraft GNC model into a debugging exercise. Students test incorrect and corrected model structures, observe the response, and learn why each fix matters.
The lab follows the same reasoning used in real engineering work: checking state propagation, validating bus interfaces, tuning attitude control, and testing chaser–target behaviour.
- Compare incorrect and correct rotational dynamics
- Check whether the SatelliteBus exposes the full spacecraft state
- Understand why attitude control needs both \( \theta \) and \( \omega \)
- Explore how PD gains affect damping, stability, and response
- Test how a chaser spacecraft responds while approaching a target
This lab connects:
model structure → simulation → failure → debugging → control design → engineering insight- Why Euler angles become difficult near singular configurations
- How body rates are integrated into attitude updates in practice
- What rigid-body motion reveals about principal-axis stability
Planned problems in this section will emphasize representation choice, notation clarity, and how rotational equations are translated into computation.
- How orbital elements map into position–velocity state vectors
- What makes a Hohmann transfer fuel-efficient, and when it is not enough
- How relative satellite motion evolves under Clohessy–Wiltshire assumptions
This section will gradually shift from topic labels to mission-style questions, with stronger emphasis on assumptions, geometry, and engineering trade-offs.
- When gravity-gradient stabilization is useful and what its limits are
- How a reaction wheel maneuver is planned from torque and inertia constraints
- Interactive GNC debugging lab: rotational dynamics, SatelliteBus checks, attitude control, and relative navigation
Problems here will be expanded to include interpretation of control behaviour, simplifying assumptions, and links between equations, simulation, and implementation.
- Begin with a few high-quality flagship worked problems
- Use clear notation, explicitly stated assumptions, and code-linked reasoning
- Prioritize depth, engineering judgment, and physical interpretation
- Expand gradually only after the first case studies are fully developed