Rocket Launch Dynamics: Gimbal Attitude Control & Max-Q (2D)

This 2D companion looks at the launch problem the 3D version does not model at all: keeping the vehicle pointed the right way. A real proportional-derivative gimbal controller commands the engine's thrust-vector angle every physics step to fight the aerodynamic instability created by the center of pressure sitting ahead of the center of gravity, while a wind-gust disturbance and a shrinking, lighter, easier-to-rotate vehicle (mass and moment of inertia both fall as propellant burns) change the fight throughout the ascent. Tune the gains too low, or trigger too strong a gust, and the vehicle tumbles past its structural limit — the same trade-off real launch-vehicle guidance software has to solve.