| Abstract [eng] |
In this study, a quadcopter’s mathematical model during a rocket launch is presented and analysed using MATLAB to explore the quadcopter's behaviour. The validation of the model is conducted through the dichotomy method. This comprehensive mathematical model covers pre- and post-launch scenarios, covering the kinematics, dynamics, and system linearisation. By employing MATLAB and the dichotomy method, the study simulates the quadcopter's behaviour, solving the nonlinear representations of the system. The research incorporates literature analyses on quadcopter and rocket dynamics, recoil effects, model validation, and methodological aspects, including the problem statement, mathematical model formulation, model validation employing the dichotomy method, and MATLAB implementation. While no direct studies cover the exact focus of this study, literature findings on quadcopter and rocket behaviour offer sufficient information to understand the kinematics and dynamics of the system and comprehend rocket behaviour post-launch. The mathematical model, formulated based on Newton-Euler equations and Newton’s laws of motion, captures pre- and post-launch kinematics and dynamics. It includes equations defining the system’s position and orientation in space, linear and angular velocity, total thrust, total moment, torque, rotational and translational acceleration, all linearised and presented in state space form. The model considers the quadcopter hovering at an altitude of 50 meters AGL during a rocket launch, with the rocket launched in the direction of the positive X-axis, producing a negative displacement of the quadcopter along the same axis and a downward pitch angle of 30°. Dependent variables include the quadcopter’s reaction force, velocity, and acceleration, while independent variables involve the quadcopter and rocket mass, system mass, gravitational acceleration, rocket launch altitude, and rocket launch velocities. Section 5 outlines the principles of the dichotomy method, detailing the setup of initial bounds and a convergence tolerance level. The bounds range between 50 and 60 m/s rocket velocities with increments of 0.5 m/s, with a tolerance level set at one millionth (0.000001). However, the minimum rocket launch velocity is approximately 𝜐_0_rocket_min ≈ 55 m/s, the model tests between 50 and 60 m/s, observing successful convergence of both quadcopter velocity and acceleration equations around a 59.99 m/s rocket launch velocity. Furthermore, the study explores the quadcopter’s behaviour across various rocket launch velocities within a specific timeframe, providing data on velocity, acceleration, position trajectory, total energy, and more. It concludes by noting the absence of assessment regarding stability, control systems, or trajectory movement for both quadcopter and rocket pre- and post-launch. The methodology employed ensures a systematic validation of the system’s mathematical model, with success determined by root convergence for each bound. The generated MATLAB graphs illustrate the relationship between quadcopter velocity and acceleration for specific timeframes across different rocket launch velocities in the post-launch scenario. |
