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Instructor Guide

Course fit

This lab targets a graduate flight dynamics / aerospace systems course (MSc core or PhD elective). Prerequisites: rigid-body dynamics (Euler's equations), an ODE course covering numerical integration basics, and familiarity with Python/NumPy. No prior exposure to missile/rocket aerodynamics is assumed — aerodynamic-model.md and atmosphere-model.md are written to stand alone.

Suggested schedule (7 sessions, ~2h each)

  1. Mathematical model & assumptions. Read mathematical-model.md and FM04.pdf Secs. 1-2 together. Discuss why each of the five modeling assumptions is reasonable for this problem and where it would break.
  2. Coordinate frames and Euler angles. coordinate-systems.md + Exercise 1(c). Whiteboard the 3-rotation derivation of L_BE live.
  3. Equations of motion, term by term. equations.md. Walk through equations_of_motion.py line-by-line, matching each Python line to a term in Eq. (1)/Euler's equation.
  4. Numerical integration. numerical-methods.md + Exercises 2-3 as an in-class coding session (pair programming: implement Euler, then RK4).
  5. Atmosphere and aerodynamics. atmosphere-model.md + aerodynamic-model.md. Use the GUI's Aerodynamics page live to sweep Mach and discuss the transonic hump.
  6. Sensitivity/dispersion analysis. uncertainty-analysis.md + Exercise 8 assigned as a take-home. Discuss OAT vs. global sensitivity methods.
  7. Synthesis / figure reproduction. Exercise 7 presentations — each student/group presents their reproduction of one paper figure and discusses discrepancies.

Grading rubric guidance (suggested weights)

  • Correctness of derivations (Exercise 1): 15%
  • Working RK4 implementation + validation (Exercise 2): 20%
  • Timestep/stability analysis with genuine empirical convergence-order measurement (Exercise 3): 20%
  • Model-assumptions discussion depth (Exercises 4, 6): 15%
  • Figure reproduction + discrepancy analysis (Exercise 7): 15%
  • Dispersion/Monte Carlo extension (Exercise 8): 15%

Emphasize numerical rigor over cosmetic plot-matching: a student who gets a different impact range than the paper but correctly explains why (digitized-coefficient caveat, different elevation angle used in the worked example, etc.) should score higher than one who does not acknowledge the discrepancy at all.

Known pitfalls to warn students about

  • Table 1 digitization caveat. Make sure students read the caveat in aerodynamic-model.md before spending hours trying to exactly match the paper's numeric figures — the source PDF's coefficient table is corrupted by OCR/extraction and this repo's values are a stand-in.
  • Elevation angle mismatch. The paper's worked trajectory example (Figs. 2-9) uses a 50° firing angle; this repo's defaults use 45° unless changed. Range/time-of-flight will differ for that reason alone.
  • Gimbal lock at steep launch angles. Very high elevation angles (near 90°) will show numerical artifacts from the Euler-angle kinematic singularity (Exercise 5) — this is expected and pedagogically useful, not a bug to "fix" by brute force.

Extending the lab

The codebase is intentionally modular (rocket.py, atmosphere.py, aerodynamics.py, frames.py, equations_of_motion.py, integrators.py, simulate.py, dispersion.py) so instructors can swap in:

  • a different rocket's mass/geometry (new RocketParams),
  • a real Missile Datcom output table (replace aerodynamics.py's tables),
  • a higher-fidelity atmosphere (e.g. full 1976 USSA up to 86 km),
  • a quaternion-based kinematics module (Exercise 5's stretch goal),

without touching the rest of the pipeline.