Vertical Launch Trajectory Simulation Program (Using Quaternion Method)

Vertical launch trajectory simulation programs are commonly used to model the flight path and attitude variations of missiles or rockets during their vertical launch phase. By employing the quaternion method for attitude description, this approach effectively avoids potential gimbal lock issues associated with traditional Euler angles while maintaining numerical stability in calculations.

Core Methodology Kinematic Modeling The vertical launch trajectory typically consists of boost phase and inertial flight phase. The program establishes six-degree-of-freedom motion equations including state variables such as position, velocity, and angular rates. Quaternions describe the rotational relationship between the body frame and ground frame, with attitude updates performed through quaternion differential equations.

Quaternion Method Advantages Compared to Euler angles, quaternions require only four parameters (one real component + three imaginary components). They enable continuous rotation through quaternion multiplication, offering higher computational efficiency without singularities. The simulation requires quaternion normalization to maintain unit quaternion properties.

MATLAB Implementation Key Points Use ODE solvers (such as `ode45`) for numerical integration of motion equations. Convert thrust and aerodynamic forces from body frame to ground frame using direction cosine matrices (generated from quaternions). Visualization components can plot 3D trajectory curves and real-time attitude variations.

Extension Applications This methodology can be extended to multi-stage rocket separation simulations and guidance law validation scenarios. When combined with Monte Carlo simulations, it can further analyze launch disturbance impacts. For incorporating wind field disturbances or elastic vibrations, additional terms can be added to the dynamic equations.