Vertical Launch Ballistic Simulation Program (Using Quaternion Method)

The vertical launch trajectory simulation program (using quaternion method) is written in MATLAB. This program implements advanced quaternion mathematics to accurately simulate projectile motion in three-dimensional space, accounting for critical physical factors including aerodynamic drag forces, gravitational effects, and rotational dynamics. The implementation utilizes quaternion algebra for orientation representation, which avoids gimbal lock issues and provides numerical stability during extended simulations. Key algorithm features include: Quaternion-based rotation matrices for coordinate transformations, Fourth-order Runge-Kutta integration for solving differential equations of motion, and atmospheric density models for altitude-dependent drag calculations. The simulation framework can model various scenarios such as missile launch sequences, rocket trajectories, and pyrotechnic displays with high precision. The code architecture employs modular design with separate functions for: quaternion normalization and multiplication operations, force and moment calculations based on current states, and real-time visualization of 3D trajectory data. This program enables researchers and engineers to analyze projectile behavior under different conditions, validate control system designs, and optimize launch parameters through comprehensive parametric studies.