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The vertical launch trajectory simulation program (using quaternion method) is written in Matlab. This program is designed to accurately simulate the movement of a projectile launched vertically, taking into account factors such as air resistance and gravity. It can be used to model a variety of scenarios, including missile launches and fireworks displays. The program utilizes the quaternion method, which is a mathematical technique used to represent rotations in three-dimensional space. This method provides a more efficient and accurate way to calculate the orientation of the projectile as it moves through the air. By using this program, researchers and engineers can gain valuable insights into the behavior of projectiles and improve the design of launch systems.