Calculation of the deflection in the lemniscate of Bernoulli. Application to railway transfer curves
Abstract
Analytical expressions are deduced to calculate the deflection between a chord and a lemniscate curve. In railways, the interest of these expressions is that lemniscates are used as transfer curves between a straight and a circular section. Moreover, according to the regulations, the deflection that separates a wagon from the track must not exceed a certain amount, so that the expressions deduced are very useful in routine checks of railway tracks.
References
Blanch L, Checa E, Marín J. Una aproximación a la curva de transición Clotoide vista desde Mathematica. Modelling in Science Education and Learning. 2013;6:105-19.
Spiegel MR. Handbook of Mathematical Formulas. New York, USA: Schaum-McGraw Hill, 1968.
Oldham KB, Myland J, Spanier J. An atlas of functions: with equator, the atlas function calculator. Springer Science & Business Media, 2010.