An example of quaternion parameterization for dynamical simulations

The dynamical simulation of rigid bodies can be gathered from the classical Newton-Euler differential equations, which commonly make use of the Euler angles parametrization. In this work, the initial value problem associated with motion is presented in terms of quaternion formulation instead of the Euler one. The reason why the quaternion parametrization is proposed lies on the possibility of avoiding singularities that can occur by considering Euler angles. Moreover, the strength of quaternions is represented by the linearity of their formulation, the easiness of their algebraic structure and, overall, on their stability and efficiency. Our proposed application is the mathematical modelling of a small Unmanned Aerial Vehicle dynamics. In particular a multirotor with six blades has been taken into account, its mathematical model is deduced and a comparison between the results obtained by implementing our formulation and the classical one is produced.