Numerical calculation algorithm of attitude and movement of a boomerang

Abstract

Although boomerangs are known since more than 10000 years, the study of its explanation is quite recent. The objective of this work is to detail step by step how to get an algorithm which allows to simply compute the boomerang trajectory and attitude. In the literature, most of the time, a four wings boomerang is studied because of the simplification its symmetry induce. In this work, the ”classic” two wings boomerang is studied. As the objective it to obtain an algorithm which can be used for numerical calculation, the mathematical development is done using the concept of vectrix, the matrix representation of vectors. To avoid numerical errors the attitude in terms of Euler angles will be integrated using the quaternions theory, exactly the same way it is done to calculate satellite attitude.