Three methodologies to represent the dynamic of an aerial vehicle are presented. We mainly focus on the mathematical equations of a quadcopter. They include the classical Euler–Lagrange formalism and the Newton–Euler approach. The Euler–Lagrange methodology is essentially used for the ideal case, i.e., without perturbations and uncertainties in the model. In the Newton–Euler approach the aerodynamics and flapping effects are considered. The third methodology, the quaternions, is introduced as a new solution to solve the singularity problem that could appear in the other formalisms. In addition, aggressive maneuvers such as looping could be also studied with this technique.
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