On a tautochrone–related family of paths
R. Muñozª, G. Fernández–Anayab
ª Universidad Autónoma de la Ciudad de México, Centro Histórico, Fray Servando Teresa de Mier 92 y 99, Col. Obrera, Del. Cuauhtémoc, México D.F., 06080, México, e–mail: rodrigo.munoz@uacm.edu.mx
b Universidad Iberoamericana, Departamento de Física y Matemáticas, Av. Prolongación Paseo de la Reforma 880, Col. Lomas de Santa Fe, Del. Álvaro Obregón México D.F., 01219, México, e–mail: guillermo.fernandez@uia.mx
Recibido el 26 de julio de 2010 ]]> Aceptado el 30 de agosto de 2010
Abstract
An alternative approach to the properties of the tautochrone and brachistochrone curves is used to introduce a family of curves complying with relations where the time of descent is proportional to a fractional power of the height difference. These curves are classified acording with their symmetries. Further properties of these curves are studied.
Keywords: Analytical mechanics; Huygens's isochrone curve; Abel's mechanical problem.
Resumen
Utilizamos un tratamiento alternativo de las curvas tautocrona y braquistocrona para introducir una familia de curvas que cumplen con relaciones en las que el tiempo de descenso es directamente proporcional a la altura descendida, elevada a un valor fraccionario. Las mencionadas curvas son clasificadas de acuerdo con sus simetrías. Se estudian otras propiedades de dichas curvas.
Descriptores: Mecánica analítica; curva isocrona de Huygens; problema mecánico de Abel.
]]> PACS: 01.55.+b; 02.30Xx; 02.30.Hq; 02.30.Em
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