Mathematical modelling and simulation of a rocket’s take-off trajectory


A rocket is a vehicle that launches into space or describes a suborbital flight. It’s subjected to the forces of weight, thrust, and the aerodynamic forces, lift and drag. The relative magnitude and direction of the forces determines the flight trajectory of the rocket. The objectives of this paper are to model the rocket’s take-off trajectory and understand the tradeoff when using the main engine in conjunction with the lateral thrusters. Also, to obtain a linear model that represents the altitude obtained by the rocket in the ascending phase and to examine system behavior through stability and sensitivity analysis. Rocket’s trajectory is obtained in four situations depends on the engine or thrusters that are in operation. Linearization methods were used to replace the model by a simpler function due to the possibility of use tools for studying linear systems to analyze the behavior of a nonlinear function near a given point and because a linear model is required for certain types of analysis such as stability analysis. Finally, sensitivity analysis of the parameters of the model is used to study how the uncertainty in the output of a mathematical model can be apportioned to different sources of uncertainty in its inputs


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