El problema de la Braquistócrona en el cilindro S1 × R con varias vueltas
We briefly present the brachistochrone problem in a vertical plane. Next, we present the parametric formulation of the brachistochrone problem on the surface of a vertical cylinder of radius R, and we find the curve that solves this problem. We immediately formulate the problem of the tautochronous...
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ri-123456789-308462020-12-13T08:01:36Z El problema de la Braquistócrona en el cilindro S1 × R con varias vueltas Salazar, Hector Leny Carrion Problema del braquistócrona Cálculo variacional Soluciones con cierto número de enrolamientos We briefly present the brachistochrone problem in a vertical plane. Next, we present the parametric formulation of the brachistochrone problem on the surface of a vertical cylinder of radius R, and we find the curve that solves this problem. We immediately formulate the problem of the tautochronous in the cylinder, and we demonstrate that the brachistochrone curve found previously has tautochronous behavior, that is, two loose particles from the rest of the points other than the brachistochrone curve, reach the lowest point of the trajectory simultaneously. It is also verified that the brachistochrone curve in a vertical plane (inverted cycloid) is the limit of the brachistochrone curve found on the cylindrical surface when the radius of the cylinder tends to infinity. Later we analyze the brachistochronous problem between two fixed points A and B on the cylindrical surface with the additional condition that the particle before reaching the end point B must give a certain number of turns previously defined. We find the curve that solves this problem and additionally, we find a mathematical relationship that determines how many turns can be maximum if we set the values of the coordinates of the starting point (A), end (B), the radius of the cylinder and g (the acceleration due to gravity) Presentamos brevemente el problema del braquistócrona en un plano vertical. A seguir presentamos la formulación paramétrica del problema de la braquistócrona sobre la superficie de un cilindro vertical de radio R y encontramos la curva que resuelve este problema. Enseguida formulamos el problema del tautócrona en el cilindro y demostramos que la curva tipo braquistócrona encontrada anteriormente tiene conportamiento tautócrono, esto es, dos partículas sueltas del reposo de puntos distintos de la curva braquistócrona, llegan al punto más bajo de la trajectoria en forma simultánea. Se verifica también que la curva tipo braquistócrona en un plano vertical (cicloide invertida) es límite de la curva tipo braquistócrona encontrada en la superficie cilíndrica cuando el radio del cilindro tiende al infinito. Posteriormente analizamos el problema del braquistócrona entre dos pontos fijos A y B sobre la superficie cilíndrica con la condición adicional de que la partícula antes de llegar al punto final B deve dar um cierto número de vueltas previamente definido. Encontramos la curva que resuelve este problema y adicionalmente encontramos uma relación matemática que determina cuantos vueltas como máximo puede haber si fijamos los valores de las coordenadas del punto inicial (A), final (B), el radio del cilindro y g (la aceleración de la gravedad) 2020-12-07T12:45:45Z 2020-12-07T12:45:45Z 2020-06-04 article CARRION S., H. L.. El problema de la Braquistócrona en el cilindro S1 × R con varias vueltas. Revista Mexicana de Física E, v. 17, p. 276, 2020. Disponível em: https://rmf.smf.mx/ojs/rmf-e/article/view/5202 Acesso em: 20 nov. 2020. https://doi.org/10.31349/RevMexFisE.17.276 2683-2216 1870-3542 https://repositorio.ufrn.br/handle/123456789/30846 10.31349/RevMexFisE.17.276 es application/pdf Sociedad Mexicana de Fisica |
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Spanish / Castilian |
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Problema del braquistócrona Cálculo variacional Soluciones con cierto número de enrolamientos |
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Problema del braquistócrona Cálculo variacional Soluciones con cierto número de enrolamientos Salazar, Hector Leny Carrion El problema de la Braquistócrona en el cilindro S1 × R con varias vueltas |
description |
We briefly present the brachistochrone problem in a vertical plane. Next, we present the parametric formulation of the brachistochrone problem on the surface of a vertical cylinder of radius R, and we find the curve that solves this problem. We immediately formulate the problem of the tautochronous in the cylinder, and we demonstrate that the brachistochrone curve found previously has tautochronous behavior, that is, two loose particles from the rest of the points other than the brachistochrone curve, reach the lowest point of the trajectory simultaneously. It is also verified that the brachistochrone curve in a vertical plane (inverted cycloid) is the limit of the brachistochrone curve found on the cylindrical surface when the radius of the cylinder tends to infinity. Later we analyze the brachistochronous problem between two fixed points A and B on the cylindrical surface with the additional condition that the particle before reaching the end point B must give a certain number of turns previously defined. We find the curve that solves this problem and additionally, we find a mathematical relationship that determines how many turns can be maximum if we set the values of the coordinates of the starting point (A), end (B), the radius of the cylinder and g (the acceleration due to gravity) |
format |
article |
author |
Salazar, Hector Leny Carrion |
author_facet |
Salazar, Hector Leny Carrion |
author_sort |
Salazar, Hector Leny Carrion |
title |
El problema de la Braquistócrona en el cilindro S1 × R con varias vueltas |
title_short |
El problema de la Braquistócrona en el cilindro S1 × R con varias vueltas |
title_full |
El problema de la Braquistócrona en el cilindro S1 × R con varias vueltas |
title_fullStr |
El problema de la Braquistócrona en el cilindro S1 × R con varias vueltas |
title_full_unstemmed |
El problema de la Braquistócrona en el cilindro S1 × R con varias vueltas |
title_sort |
el problema de la braquistócrona en el cilindro s1 × r con varias vueltas |
publisher |
Sociedad Mexicana de Fisica |
publishDate |
2020 |
url |
https://repositorio.ufrn.br/handle/123456789/30846 |
work_keys_str_mv |
AT salazarhectorlenycarrion elproblemadelabraquistocronaenelcilindros1rconvariasvueltas |
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1773962186401513472 |