How do Rockets Maintain their Vertical Orientation Precisely During Launch

Rockets must maintain precise vertical orientation during launch to ensure structural integrity and mission success. This research investigates the control systems and dynamics that enable rockets to stabilize their trajectory despite external perturbations. We derive equations of motion for a rocket system, develop a state-space representation suitable for computational analysis, design an LQR (Linear Quadratic Regulator) controller to maintain vertical orientation, and validate performance across multiple scenarios. The findings demonstrate that model-based control strategies can effectively regulate rocket orientation with robustness to environmental variations.