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Suleyman şenyurt - One of the best experts on this subject based on the ideXlab platform.

Fábio Nunes Da ,silva - One of the best experts on this subject based on the ideXlab platform.

  • Superfícies regradas desenvolvíveis tipo tempo e tipo espaço no espaço de Minkowski
    2013
    Co-Authors: Fábio Nunes Da ,silva
    Abstract:

    Neste trabalho, baseado em [11], [13] e [7] estudamos superfícies regradas tipo espaço ou tipo tempo no espaço de Minkowski. Inicialmente, encontramos expressões para o triedro de Frenet de curvas tipo tempo, tipo espaço ou tipo luz. Mostramos que uma superfície regrada tipo tempo ou tipo espaço é desenvovível se, e somente se, o parâmetro de distribuição é nulo. Então, para o caso em que os vetores de Frenet da diretriz não são tipo luz, mostramos que a superfície regrada tipo espaço ou tipo tempo é desenvolvível se, e somente se, a diretriz é uma hélice. No caso em que algum dos vetores de Frenet da diretriz é tipo luz, mostramos que a superfície regrada tipo tempo ou tipo espaço é desenvolvível se, e somente se, a torção é constante. Estudamos casos especiais, nos quais a superfície regrada tipo tempo ou tipo espaço é gerada por retas que estão no plano osculador, ou no plano normal, ou no plano retificante, ou na direção de algum dos vetores do triedro de Frenet. _______________________________________________________________________________________ ABSTRACTIn thisWork, based in [11], [13] and [7] we study timelike and spacelike ruled surfaces in Minkowski space. Initially we find expressions for Frenet trihedron of lightlike, spacelike or timelike curves. We show that a timelike or spacelike ruled surface is developable if and only if the distribution parameter is null. Then for the case where some of the Frenet vectors of the Directrix aren’t lightlike, we show that the timelike ou spacelike ruled surface is developable if and only if the Directrix is helix. In the case where some of the Frenet vectors of the Directrix is lightlike, we show that the timelike or spacelike ruled surface is developable if and only if the torsion is constant. We study special cases which the timelike or spacelike ruled surface is generated for straight line that are in osculating plane, or in normal plane, or in rectifying plane, or in the direction of some of the Frenet vectors

  • Superfícies regradas desenvolvíveis tipo tempo e tipo espaço no espaço de Minkowski
    2013
    Co-Authors: Fábio Nunes Da ,silva
    Abstract:

    Dissertação (mestrado)—Universidade de Brasília, Instituto de Ciências Exatas, Departamento de Matemática, 2013.Neste trabalho, baseado em [11], [13] e [7] estudamos superfícies regradas tipo espaço ou tipo tempo no espaço de Minkowski. Inicialmente, encontramos expressões para o triedro de Frenet de curvas tipo tempo, tipo espaço ou tipo luz. Mostramos que uma superfície regrada tipo tempo ou tipo espaço é desenvovível se, e somente se, o parâmetro de distribuição é nulo. Então, para o caso em que os vetores de Frenet da diretriz não são tipo luz, mostramos que a superfície regrada tipo espaço ou tipo tempo é desenvolvível se, e somente se, a diretriz é uma hélice. No caso em que algum dos vetores de Frenet da diretriz é tipo luz, mostramos que a superfície regrada tipo tempo ou tipo espaço é desenvolvível se, e somente se, a torção é constante. Estudamos casos especiais, nos quais a superfície regrada tipo tempo ou tipo espaço é gerada por retas que estão no plano osculador, ou no plano normal, ou no plano retificante, ou na direção de algum dos vetores do triedro de Frenet. _______________________________________________________________________________________ ABSTRACTIn thisWork, based in [11], [13] and [7] we study timelike and spacelike ruled surfaces in Minkowski space. Initially we find expressions for Frenet trihedron of lightlike, spacelike or timelike curves. We show that a timelike or spacelike ruled surface is developable if and only if the distribution parameter is null. Then for the case where some of the Frenet vectors of the Directrix aren’t lightlike, we show that the timelike ou spacelike ruled surface is developable if and only if the Directrix is helix. In the case where some of the Frenet vectors of the Directrix is lightlike, we show that the timelike or spacelike ruled surface is developable if and only if the torsion is constant. We study special cases which the timelike or spacelike ruled surface is generated for straight line that are in osculating plane, or in normal plane, or in rectifying plane, or in the direction of some of the Frenet vectors

şeyda Kilicoglu - One of the best experts on this subject based on the ideXlab platform.

V. N. Ivanov - One of the best experts on this subject based on the ideXlab platform.

  • orthogonal curved coordinate system and forming the surfaces on trapezium curved plans
    Vestn. Ross. univ. družby nar. Ser. Inž. issled., 2017
    Co-Authors: V. N. Ivanov, Timur Soibnazarovich Imomnazarov, Ismael Taha Farhan Farhan
    Abstract:

    Thin space constructions on curved plans there are used at building of public structures, trade centers. Sport constructions. Working-out the methods of forming of the surfaces on the curved plans that is one of the modern task of the architecture and town building. The orthogonal coordinate system that is formed at the plane with some plane Directrix curve and the system of the right lines orthogonal to the Directrix curve there is regarded at the stat. The coordinate system forms some trapezium-curved segment. Taking some function of the vertical coordinate there is possible to receive different surfaces at the curved plans. Conjugating different Directrix curves, it’s possible to receive the combined surfaces. The article presents a system of orthogonal coordinates of curvilinear-trapezoidal planes and methods for forming surfaces on these planes. Surfaces with a function of the vertical coordinate of a general view are considered, and surfaces on combined plans of segments of the same type are shown.

  • Geometry and forming of the normal surfaceswith system of plane coordinate lines
    Peoples’ Friendship University of Russia (RUDN University), 2011
    Co-Authors: V. N. Ivanov
    Abstract:

    The surfaces with system of coordinate lines lying in normal plane of some Directrix are investigated. The vector equation of the surfaces and the formulas of the main quadratic forms are received. The drawings of surfaces made in MathCad system with different Directrix and genetrix lines are show

  • Some aspects of the geometry of the surfaces with the system of plane coordinate lines
    Peoples’ Friendship University of Russia (RUDN University), 2010
    Co-Authors: V. N. Ivanov
    Abstract:

    In the article, the geometry of the surfaces with the system of the plane coordinate lines is investigated. The common vector formula of these surfaces is received. The formulas of the coefficients of the quadratic forms are presented too. The conditions, when of the plane coordinate lines are lines of the principle curvatures of the surface, are received. The subclass of the surfaces with the system of the plane coordinate lines in the normal plane of the Directrix curve is investigated. The formula of the Monge's ruled surfaces is received on the base of the common formula. The drawings of the Monge's ruled surfaces made in MathСad system are shown

Sánchez José - One of the best experts on this subject based on the ideXlab platform.

  • La bóveda de hormigón del Club Táchira en Caracas
    'Editorial CSIC', 2005
    Co-Authors: Escrig Félix, Sánchez José
    Abstract:

    In the summer of 1955, the Venezuelan architect Fruto Vivas met up with the engineer Eduardo Torroja in Costillares (Madrid) in order to propose collaborating on the design of a roof. The form of the shell did not come to Torroja in a complete form, but rather he had to approach it based on discussions with the author. The previous design was the sinuous form, which would be generated by a pair of curves. One a curved Directrix of a warped trigonometric line, and the other a flat catenary, which moves parallel to itself with the vertex always, situated above the curved Directrix. The complex process of the design and the details of the project are explained in detail as well as the complex reduced model build to test the analytical calculus. After all we have compared the original outputs that Torroja obtained wit the results of a Finite Element Method. The conclusions can been summarized in the difficulty of establish a direct correspondence between both methods.En el verano de 1955, el arquitecto venezolano Fruto Vivas, se reunio con el Ingeniero Eduardo Torroja en Costillares (Madrid) para plantearle la colaboración en el diseño de una cubierta. La forma de la cáscara no convenció a Torroja, sin embargo él la ajustó basándose en discusiones con el autor. El diseño previo tenía una forma sinuosa, que se generaba por un par de curvas. Una curva directriz de tipo trigonométrico alabeado y otra de forma catenaria plana, que se desplaza paralelamente a si misma con el vértice situado siempre sobre la curva directriz. El complejo proceso de diseño y los detalles del proyecto se explican detalladamente, así como el modelo reducido construido para ensayar el cálculo analítico. Después de todo comparamos los datos que obtiene Torroja con los resultados del método de cálculo por elementos finitos. Las conclusiones pueden ser resumidas en la dificultad para establecer una correspondencia directa entre ambos métodos