El diseño de la Montaña Rusa involucra una secuencia de curvas que deben ser unidas suavemente cuya parametrización facilita el estudio de sus propiedades. En este artículo se estudia la curvatura de la trayectoria que seguiría un vehículo en la atracción mecánica.Observando que los cambios discontinuos en la curvatura a lo largo de la trayectoria implican cambios en la aceleración normal que podrían ser inseguros para los pasajeros se buscó una parametrización diferente. Al considerar una trayectoria cuya curvatura cambia linealmente con el desplazamiento se encuentra que la espiral de Euler permite conectar suavemente diferentes segmentos de la trayectoria y diseñar atracciones mecánicas más seguras. Finalmente se compara la parametrización obtenida con la trayectoria de la atracción Doble Loop del parque de diversiones Salitre Mágico de Bogotá, encontrando que su trayectoria está formada por secuencias de arcos de circunferencia y secciones de la espiral de Euler.

We consider the dynamics of the Sorkin-Johnston (SJ) state for a massless scalar field in two dimensions. We conduct a study of the renormalized stress-tensor by a subtraction procedure, and compare the results with those of the conformal vacuum, with an important contribution from correction term. We find a large trace anomaly and compute backreaction effects to two dimensional (Liouville) gravity. We find a natural interpretation for the mirror behavior of the SJ state described in previous works.

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The problem of the classical motion of a round object is typically presented using idealized setups in order to make it more tractable. Popular examples include a sphere moving on a perfectly flat inclined plane. Here, we focus on a rolling object and show that more realistic cases of curved surfaces defined by a single variable and including friction are not only tractable, but also offer new physics. We show that the point at which the object may detach from the surface can be predicted accurately using simple methods. We check the accuracy of our theoretical calculations by performing experiments using tracks in the shape of four different conic curves. We observe very good agreement between the theoretical predictions and the experimental results. Our findings not only suggest that curved surfaces can be included in the presentation of motion to students, but that they also offer intriguing new scenarios for gaining physical insight.