La espiral de Euler en la montaña rusa.

The design of the roller coaster involves a sequence of curves that must be connected 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, and then a parameterization for a trajectory whose curvature is continuous was sought. When we consider a trajectory whose curvature changes linearly with the displacement, it is found that the Euler spiral allows smoothly connecting different segments of the trajectory and describing safer mechanical attractions. Finally, the parameterization obtained is compared with the trajectory of the Double Loop attraction in the Salitre Mágico amusement park in Bogota, finding that its path is formed by sequences of circumference arcs and sections of the Euler spiral. [ABSTRACT FROM AUTHOR]