La espiral de Euler en la montaña rusa - García-Matos, Javier Camilo; Avilán-Vargas, Nicolás (Revista Científica, 2019)
The design of the roller coaster involves a sequence of curves that must be united smoothly, whose parameterization enables the study of its properties. In this paper we study the curvature of the trajectory that a vehicle would follow in mechanical attraction. The discontinuous changes in the curvature along the trajectory imply changes in the normal acceleration that could be unsafe for the passengers, a different parameterization was sought. When we consider a trajectory whose curvature changes linearly with the displacement, it is found that the Euler spiral allows to smoothly connect different segments of the trajectory and design safer mechanical attractions. Finally, the parametrization obtained is compared with the trajectory of the Double Loop attraction in the Salitre Mágico amusement park in Bogotá, finding that its path is formed by sequences of circumferece arcs and sections of the Euler spiral.