Artículos de revistas
Uso de programacion lineal para conocer los parametros geometrícos de superficies cónicas convexas
Autor
CASTAÑEDA ROLDÁN, C.
NIVON SANTIAGO, R.
SANTIAGO ALVARADO, A.
VÁZQUEZ MONTIEL, S.
Institución
Resumen
EN ESTE TRABAJO SE PROPONE UN MÉTODO PARA CONOCER LA FORMA ANALÍTICA DE UNA SUPERFICIE ÓPTICA CONVEXA, A PARTIR DE LAS COORDENADAS DE ALGUNOS PUNTOS MEDIDOS SOBRE ESTA. ES DECIR, ENCONTRAR LA FORMA ANALÍTICA DE LA SUPERFICIE QUE MEJOR SE AJUSTA A UNA DISTRIBUCIÓN DE PUNTOS MEDIDOS SOBRE LA SUPERFICIE QUE SE DESEA CARACTERIZAR ( EN PARTICULAR, SE DESEA APLICAR AL ESPEJO SECUNDARIO DEL GRAN TELESCOPIO MILIMÉTRICO, QUE ES UNA SUPERFICIE CÓNICA CONVEXA DE 2.57 M DE DIÁMETRO, CONSTANTE DE CONICIDAD K=-1.14 Y F /0.4). EL MÉTODO CONSISTE EN RESOLVER EL PROBLEMA DE AJUSTE COMO UN PROBLEMA DE APROXIMACIÓN POLINOMIAL EN NORMA UNIFORME, EL CUAL SE RESUELVE POR MEDIO DE PROGRAMACIÓN LINEAL. FINALMENTE SE PRESENTAN LOS RESULTADOS OBTENIDOS AL EVALUAR ALGUNAS SUPERFICIES CÓNICAS CON EL MÉTODO PROPUESTO.AbstractIN THIS PAPER WE PROPOSED A METHOD TO OBTAIN THE ANALYTIC SHAPE OF AN OPTICAL CONVEX SURFACE STARTING FROM THE COORDINATES OF SOME POINTS MEASURED ON THE SURFACE. IN OTHER WORDS, WE WANT TO FIND THE ANALYTIC SHAPE OF THE SURFACE THAT BEST FITS A DISTRIBUTION OF POINTS MEASURED ON A SURFACE (IN PARTICULAR, WE WANT TO APPLY THE METHOD TO THE SECONDARY MIRROR OF THE LARGE MILLIMETER TELESCOPE; THIS MIRROR IS A CONVEX SURFACE OF 2.57 M DIAMETER, CONIC CONSTANT K= -1, AND F/0.4). THE METHOD CONSISTS OF SOLVING THE ADJUSTMENT PROBLEM AS A PROBLEM OF POLYNOMIAL APPROXIMATION IN UNIFORM NORM AND IT IS SOLVED BY MEANS OF LINEAR PROGRAMMING. FINALLY, WE PRESENT THE RESULT OBTAINED WHEN WE EVALUATE SOME CONICAL SURFACES WITH THE PROPOSED METHOD. IN THIS PAPER WE PROPOSED A METHOD TO OBTAIN THE ANALYTIC SHAPE OF AN OPTICAL CONVEX SURFACE STARTING FROM THE COORDINATES OF SOME POINTS MEASURED ON THE SURFACE. IN OTHER WORDS, WE WANT TO FIND THE ANALYTIC SHAPE OF THE SURFACE THAT BEST FITS A DISTRIBUTION OF POINTS MEASURED ON A SURFACE (IN PARTICULAR, WE WANT TO APPLY THE METHOD TO THE SECONDARY MIRROR OF THE LARGE MILLIMETER TELESCOPE; THIS MIRROR IS A CONVEX SURFACE OF 2.57 M DIAMETER, CONIC CONSTANT K= -1, AND F/0.4). THE METHOD CONSISTS OF SOLVING THE ADJUSTMENT PROBLEM AS A PROBLEM OF POLYNOMIAL APPROXIMATION IN UNIFORM NORM AND IT IS SOLVED BY MEANS OF LINEAR PROGRAMMING. FINALLY, WE PRESENT THE RESULT OBTAINED WHEN WE EVALUATE SOME CONICAL SURFACES WITH THE PROPOSED METHOD.