The Experts below are selected from a list of 247725 Experts worldwide ranked by ideXlab platform
Cribillero Zevallos, Deyvis Irving - One of the best experts on this subject based on the ideXlab platform.
-
Síntesis de un mecanismo de cuatro eslabones para una silla de descanso usando el método de Newton-Raphson
Universidad Nacional de Trujillo, 2019Co-Authors: Cribillero Zevallos, Deyvis IrvingAbstract:El presente trabajo titulado “Síntesis de un mecanismo de cuatro eslabones para una silla de descanso usando el método de Newton-Raphson”, se desarrolló utilizando la ecuación de Freudenstein para obtener las dimensiones óptimas de un mecanismo de cuatro barras en una silla de descanso, y garantizar la estabilidad en las posiciones extremas de la silla. Los ángulos 1, 2 y 4 de los eslabones del mecanismo fueron tomados en base a la ergonomía de una silla de descanso y teniendo en cuenta la anatomía del cuerpo humano (espalda, piernas y brazos) La síntesis del mecanismo fue planteada en la ecuación de Freudenstein para un mecanismo de cuatro eslabones, a la que se le aplicó el método de los mínimos cuadrados para minimizar el error en las posiciones deseadas (2 y 4) de los eslabones. Se obtiene un sistema de ecuaciones no lineales aplicando la derivada parcial con respecto a las constantes k de Freudenstein a la función que define las posiciones del mecanismo. Este sistema de ecuaciones no lineales se resolvió con el método de Newton Raphson. Las raíces de este sistema de ecuaciones no lineales (1, 2 y 3) son las longitudes de los eslabones del mecanismo de cuatro barras. Para usar este método en un sistema de ecuaciones no lineales se usó las series de Taylor debido a que son las que permiten llegar a la ecuación iterativa que resolverá el sistema de ecuaciones no lineales. El método de Newton Raphson se aplicó para 2 = 110°, 125°, 140°, 155°, 165° ; 4 = 97°, 116°, 134°, 153°, 165° y 1 = 10° determinando así los valores de 1, 2 y 3. Se realizó el código de programación en Matlab del método Newton Raphson. Se tomaron 5 posiciones angulares para 2 y 4. Una tolerancia o error de 0.0001, un máximo de iteraciones de 100(c=100) y partiendo de un vector inicial k0= (1, 1,1) que son valores iniciales de las constantes k con los cuales se va a iniciar el proceso de iteración. El programa convergió a las 12 iteraciones dando como resultado las longitudes óptimas del mecanismo de cuatro eslabones para una silla de descanso (r1=52 cm), (r2=15.3787 cm), (r3=55.4466 cm), (r4=11.5684 cm). El perfil seleccionado es una tubería ASTM 513 con un espesor 1.2mm y diámetro de ¾”. Se hizo un análisis de estabilidad para soportar el peso de una persona de 100kg. El factor de seguridad obtenido es 1.5TesisThe present work entitled "Synthesis of a four-link mechanism for a rest chair using the Newton-Raphson method", was developed using the Freudenstein equation to obtain the optimal dimensions of a four-bar mechanism in a rest chair, and ensure stability in the extreme positions of the chair. The angles 1, 2 and 4 of the links of the mechanism were taken based on the ergonomics of a resting chair and taking into account the anatomy of the human body (back, legs and arms) The synthesis of the mechanism was proposed in the Freudenstein equation for a fourlink mechanism, to which the least-squares method was applied to minimize the error in the desired positions (2 and 4) of the links. A system of non-linear equations is obtained by applying the partial derivative with respect to the k constants of Freudenstein to the function that defines the positions of the mechanism. This system of nonlinear equations was solved with the Newton Raphson method. The roots of this system of non-linear equations (1, 2 and 3) are the lengths of the links of the four-bar mechanism. To use this method in a system of nonlinear equations Taylor series were used because they are what allow us to arrive at the iterative equation that will solve system of nonlinear equations. The Newton Raphson method was applied at 2 = 110°, 125°, 140°, 155° , 165° ; 4 = 97°, 116°, 134°, 153°, 165° and 1 = 10° to determine the values of 1, 2 y 3. The programming code was made in Matlab of the Newton Raphson method. We took 5 angular positions for 2 and 4. A tolerance or error of 0.0001, a maximum of iterations of 100 (c = 100) and starting from an initial vector k0 = (1, 1, 1) that are initial values of the constants k with which the process is going to start of iteration. The program converged to the 12 iterations resulting in the optimum lengths of the four-link mechanism for a rest chair (r1 = 52 cm), (r2 = 15.3787 cm), (r3 = 55.4466 cm), (r4 = 11.5684 cm). The selected profile is an ASTM 513 pipe with a thickness of 1.2mm and a diameter of ¾ ". A stability analysis was made to support the weight of a 100kg person. The safety factor obtained is 1.
-
Síntesis de un mecanismo de cuatro eslabones para una silla de descanso usando el método de Newton-Raphson
Universidad Nacional de Trujillo, 2019Co-Authors: Cribillero Zevallos, Deyvis IrvingAbstract:El presente trabajo titulado “Síntesis de un mecanismo de cuatro eslabones para una silla de descanso usando el método de Newton-Raphson”, se desarrolló utilizando la ecuación de Freudenstein para obtener las dimensiones óptimas de un mecanismo de cuatro barras en una silla de descanso, y garantizar la estabilidad en las posiciones extremas de la silla. Los ángulos 1, 2 y 4 de los eslabones del mecanismo fueron tomados en base a la ergonomía de una silla de descanso y teniendo en cuenta la anatomía del cuerpo humano (espalda, piernas y brazos) La síntesis del mecanismo fue planteada en la ecuación de Freudenstein para un mecanismo de cuatro eslabones, a la que se le aplicó el método de los mínimos cuadrados para minimizar el error en las posiciones deseadas (2 y 4) de los eslabones. Se obtiene un sistema de ecuaciones no lineales aplicando la derivada parcial con respecto a las constantes k de Freudenstein a la función que define las posiciones del mecanismo. Este sistema de ecuaciones no lineales se resolvió con el método de Newton Raphson. Las raíces de este sistema de ecuaciones no lineales (1, 2 y 3 ) son las longitudes de los eslabones del mecanismo de cuatro barras. Para usar este método en un sistema de ecuaciones no lineales se usó las series de Taylor debido a que son las que permiten llegar a la ecuación iterativa que resolverá el sistema de ecuaciones no lineales. El método de Newton Raphson se aplicó para 2 = 110°, 125°, 140°, 155° , 165° ; 4 = 97°, 116°, 134°, 153°, 165° y 1 = 10° determinando así los valores de 1, 2 y 3 . Se realizó el código de programación en Matlab del método Newton Raphson. Se tomaron 5 posiciones angulares para 2 y 4. Una tolerancia o error de 0.0001, un máximo de iteraciones de 100(c=100) y partiendo de un vector inicial k0= (1, 1,1) que son valores iniciales de las constantes k con los cuales se va a iniciar el proceso de iteración. El programa convergió a las 12 iteraciones dando como resultado las longitudes óptimas del mecanismo de cuatro eslabones para una silla de descanso (r1=52 cm), (r2=15.3787 cm), (r3=55.4466 cm), (r4=11.5684 cm).TesisThe present work entitled "Synthesis of a four-link mechanism for a rest chair using the Newton-Raphson method", was developed using the Freudenstein equation to obtain the optimal dimensions of a four-bar mechanism in a rest chair, and ensure stability in the extreme positions of the chair. The angles 1, 2 and 4 of the links of the mechanism were taken based on the ergonomics of a resting chair and taking into account the anatomy of the human body (back, legs and arms) The synthesis of the mechanism was proposed in the Freudenstein equation for a fourlink mechanism, to which the least-squares method was applied to minimize the error in the desired positions (2 and 4) of the links. A system of non-linear equations is obtained by applying the partial derivative with respect to the k constants of Freudenstein to the function that defines the positions of the mechanism. This system of nonlinear equations was solved with the Newton Raphson method. The roots of this system of non-linear equations (1, 2 and 3) are the lengths of the links of the four-bar mechanism. To use this method in a system of nonlinear equations Taylor series were used because they are what allow us to arrive at the iterative equation that will solve system of nonlinear equations. The Newton Raphson method was applied at 2 = 110°, 125°, 140°, 155° , 165° ; 4 = 97°, 116°, 134°, 153°, 165° and 1 = 10° to determine the values of 1, 2 y 3. The programming code was made in Matlab of the Newton Raphson method. We took 5 angular positions for 2 and 4. A tolerance or error of 0.0001, a maximum of iterations of 100 (c = 100) and starting from an initial vector k0 = (1, 1, 1) that are initial values of the constants k with which the process is going to start of iteration. The program converged to the 12 iterations resulting in the optimum lengths of the four-link mechanism for a rest chair (r1 = 52 cm), (r2 = 15.3787 cm), (r3 = 55.4466 cm), (r4 = 11.5684 cm). The selected profile is an ASTM 513 pipe with a thickness of 1.2mm and a diameter of ¾ ". A stability analysis was made to support the weight of a 100kg person. The safety factor obtained is 1.
Euaggelos E Zotos - One of the best experts on this subject based on the ideXlab platform.
-
on the newton raphson basins of convergence of the out of plane equilibrium points in the copenhagen problem with oblate primaries
International Journal of Non-linear Mechanics, 2018Co-Authors: Euaggelos E ZotosAbstract:Abstract The Copenhagen case of the circular restricted three-body problem with oblate primary bodies is numerically investigated by exploring the Newton–Raphson basins of convergence, related to the out-of-plane equilibrium points. The evolution of the position of the libration points is determined, as a function of the value of the oblateness coefficient. The attracting regions, on several types of two-dimensional planes, are revealed by using the multivariate Newton–Raphson iterative method. We perform a systematic and thorough investigation in an attempt to understand how the oblateness coefficient affects the geometry of the basins of convergence. The convergence regions are also related with the required number of iterations and also with the corresponding probability distributions. The degree of the fractality is also determined by calculating the fractal dimension and the basin entropy of the convergence planes.
-
fractal basins of convergence of libration points in the planar copenhagen problem with a repulsive quasi homogeneous manev type potential
International Journal of Non-linear Mechanics, 2018Co-Authors: Sanam Suraj, Euaggelos E Zotos, Charanpreet Kaur, Rajiv Aggarwal, Amit MittalAbstract:Abstract The Newton–Raphson basins of convergence, corresponding to the coplanar libration points (which act as attractors), are unveiled in the Copenhagen problem, where instead of the Newtonian potential and forces, a quasi-homogeneous potential created by two primaries is considered. The multivariate version of the Newton–Raphson iterative scheme is used to reveal the attracting domain associated with the libration points on various type of two-dimensional configuration planes. The correlations between the basins of convergence and the corresponding required number of iterations are also presented and discussed in detail. The present numerical analysis reveals that the evolution of the attracting domains in this dynamical system is very complicated, however, it is a worth studying issue.
-
investigating the newton raphson basins of attraction in the restricted three body problem with modified newtonian gravity
Journal of Applied Mathematics and Computing, 2018Co-Authors: Euaggelos E ZotosAbstract:The planar circular restricted three-body problem with modified Newtonian gravity is used in order to determine the Newton–Raphson basins of attraction associated with the equilibrium points. The evolution of the position of the five Lagrange points is monitored when the value of the power p of the gravitational potential of the second primary varies in predefined intervals. The regions on the configuration (x, y) plane occupied by the basins of attraction are revealed using the multivariate version of the Newton–Raphson iterative scheme. The correlations between the basins of convergence of the equilibrium points and the corresponding number of iterations needed for obtaining the desired accuracy are also illustrated. We conduct a thorough and systematic numerical investigation by demonstrating how the dynamical quantity p influences the shape as well as the geometry of the basins of attractions. Our results strongly suggest that the power p is indeed a very influential parameter in both cases of weaker or stronger Newtonian gravity.
-
Basins of attraction of equilibrium points in the planar circular restricted five-body problem
Astrophysics and Space Science, 2018Co-Authors: Euaggelos E Zotos, Md Sanam SurajAbstract:We numerically explore the Newton-Raphson basins of convergence, related to the libration points (which act as attractors), in the planar circular restricted five-body problem (CR5BP). The evolution of the position and the linear stability of the equilibrium points is determined, as a function of the value of the mass parameter. The attracting regions, on several types of two dimensional planes, are revealed by using the multivariate version of the classical Newton-Raphson iterative method. We perform a systematic investigation in an attempt to understand how the mass parameter affects the geometry as well as the degree of fractality of the basins of attraction. The regions of convergence are also related with the required number of iterations and also with the corresponding probability distributions.
-
basins of convergence of equilibrium points in the pseudo newtonian planar circular restricted three body problem
Astrophysics and Space Science, 2017Co-Authors: Euaggelos E ZotosAbstract:The Newton-Raphson basins of attraction, associated with the libration points (attractors), are revealed in the pseudo-Newtonian planar circular restricted three-body problem, where the primaries have equal masses. The parametric variation of the position as well as of the stability of the equilibrium points is determined, when the value of the transition parameter $\epsilon $ varies in the interval $[0,1]$ . The multivariate Newton-Raphson iterative scheme is used to determine the attracting domains on several types of two-dimensional planes. A systematic and thorough numerical investigation is performed in order to demonstrate the influence of the transition parameter on the geometry of the basins of convergence. The correlations between the basins of attraction and the corresponding required number of iterations are also illustrated and discussed. Our numerical analysis strongly indicates that the evolution of the attracting regions in this dynamical system is an extremely complicated yet very interesting issue.
Thanatchai Kulworawanichpong - One of the best experts on this subject based on the ideXlab platform.
-
multi train modeling and simulation integrated with traction power supply solver using simplified newton raphson method
Journal of Modern Transportation, 2015Co-Authors: Thanatchai KulworawanichpongAbstract:Multi-train modeling and simulation plays a vital role in railway electrification during operation and planning phase. Study of peak power demand and energy consumed by each traction substation needs to be determined to verify that electrical energy flowing in its railway power feeding system is appropriate or not. Gauss–Seidel, conventional Newton–Raphson, and current injection methods are well-known and widely accepted as a tool for electrical power network solver in DC railway power supply study. In this paper, a simplified Newton–Raphson method has been proposed. The proposed method employs a set of current-balance equations at each electrical node instead of the conventional power-balance equation used in the conventional Newton–Raphson method. This concept can remarkably reduce execution time and computing complexity for multi-train simulation. To evaluate its use, Sukhumvit line of Bangkok transit system (BTS) of Thailand with 21.6-km line length and 22 passenger stopping stations is set as a test system. The multi-train simulation integrated with the proposed power network solver is developed to simulate 1-h operation service of selected 5-min headway. From the obtained results, the proposed method is more efficient with approximately 18 % faster than the conventional Newton–Raphson method and just over 6 % faster than the current injection method.
-
simplified newton raphson power flow solution method
International Journal of Electrical Power & Energy Systems, 2010Co-Authors: Thanatchai KulworawanichpongAbstract:Abstract This paper presents a simplified version of the well-known Newton–Raphson power-flow solution method, which is based on the current balance principle to formulate a set of nonlinear equations. Although there exist several powerful power flow solvers based on the standard Newton–Raphson (NR) method, their corresponding problem formulation is not simple due to the need for calculation of derivatives in their Jacobian matrix. The proposed method employs nonlinear current mismatch equations instead of the commonly-used power mismatches to simplify overall equation complexity. Derivation of Jacobian matrix’s updating formulae is illustrated in comparison with those of the standard Newton–Raphson method. To demonstrate its use, a simple 3-bus power system was selected as a numerical example. The effectiveness of the proposed method was examined by computer simulations through five test systems: (1) 5-bus test system, (2) 6-bus test system, (3) 24-bus IEEE test system, (4) 30-bus IEEE test system and (5) 57-bus IEEE test system. Its convergence and calculation time were observed carefully and compared with solutions obtained by the standard NR power flow method. The results show that the proposed NR method spends less execution time than the standard method does with similar convergence characteristics.
Herri Gusmedi - One of the best experts on this subject based on the ideXlab platform.
-
Vector Form Implementation in Three-Phase Power Flow Analysis Based on Power Injection Rectangular Coordinate
JURNAL NASIONAL TEKNIK ELEKTRO, 2019Co-Authors: Lukmanul Hakim, Fandi Prayoga, Khairudin Khairudin, Herri GusmediAbstract:This paper aims to propose the vector form implementation into three-phase power flow analysis. The developed algorithm is based on Newton-Raphson method with voltage is represented in rectangular coordinate. The Python programming language and its mathematical libraries are used in this works. Three-phase power flow analysis in vector form utilizes sparse matrix ordering algorithm, so the elements of the coefficient correction matrix can be rearranged easily. This method was used to solve three-phase power flow for balance or unbalance network in two actual distribution system feeders in Lampung, i.e. 119 nodes and 191 nodes. Comparison with traditional Newton-Raphson method (non-vector) shows the vector form is able to solve computation up to eight times faster than non-vector. Keywords : Three-phase power flow, Vector form, Newton-Raphson, Rectangular, Python
-
Vector Form Implementation in Three-Phase Power Flow Analysis Based on Power Injection Rectangular Coordinate
Universitas Andalas, 2019Co-Authors: Lukmanul Hakim, Fandi Prayoga, Khairudin Khairudin, Herri GusmediAbstract:This paper aims to propose the vector form implementation into three-phase power flow analysis. The developed algorithm is based on Newton-Raphson method with voltage is represented in rectangular coordinate. The Python programming language and its mathematical libraries are used in this works. Three-phase power flow analysis in vector form utilizes sparse matrix ordering algorithm, so the elements of the coefficient correction matrix can be rearranged easily. This method was used to solve three-phase power flow for balance or unbalance network in two actual distribution system feeders in Lampung, i.e. 119 nodes and 191 nodes. Comparison with traditional Newton-Raphson method (non-vector) shows the vector form is able to solve computation up to eight times faster than non-vector
Hill Betancourt, Alan F - One of the best experts on this subject based on the ideXlab platform.
-
Solución bidimensional sin malla de la ecuación no lineal de convección-difusión-reacción mediante el método de Interpolación Local Hermítica
'Universidad EAFIT', 2019Co-Authors: Bustamante Chaverra, Carlos A, Power Henry, Florez Escobar Whady, Hill Betancourt, Alan FAbstract:A meshless numerical scheme is developed for solving a generic version of the non-linear convection-diffusion-reaction equation in two-dimensional domains. The Local Hermitian Interpolation (LHI) method is employed for the spatial discretization and several strategies are implemented for the solution of the resulting non-linear equation system, among them the Picard iteration, the Newton Raphson method and a truncated version of the Homotopy Analysis Method (HAM). The LHI method is a local collocation strategy in which Radial Basis Functions (RBFs) are employed to build the interpolation function. Unlike the original Kansa’s Method, the LHI is applied locally and the boundary and governing equation differential operators are used to obtain the interpolation function, giving a symmetric and non-singular collocation matrix. Analytical and Numerical Jacobian matrices are tested for the Newton-Raphson method and the derivatives of the governing equation with respect to the homotopy parameter are obtained analytically. The numerical scheme is verified by comparing the obtained results to the one-dimensional Burgers’ and two-dimensional Richards’ analytical solutions. The same results are obtained for all the non-linear solvers tested, but better convergence rates are attained with the Newton Raphson method in a double iteration scheme.Se desarrolla un esquema numérico sin malla para resolver una versión genérica de la ecuación no lineal de convección-difusión-reacción en dominios bidimensionales. El método de Interpolación Hermitiana Local (LHI) se emplea para la discretización espacial y se implementan varias estrategias para la solución del sistema de ecuaciones no lineal resultante, entre ellas la iteración Picard, el método Newton Raphson y una versión truncada del Método de Análisis de Homotopía. (JAMÓN). El método LHI es una estrategia de colocación local en la que se utilizan funciones de base radial (RBF) para construir la función de interpolación. A diferencia del método original de Kansa, el LHI se aplica localmente y los operadores diferenciales de ecuación límite y gobernante se utilizan para obtener la función de interpolación, dando una matriz de colocación simétrica y no singular. Las matrices analíticas y numéricas jacobianas se prueban para el método de Newton-Raphson y las derivadas de la ecuación de gobierno con respecto al parámetro de homotopía se obtienen analíticamente. El esquema numérico se verifica comparando los resultados obtenidos con las soluciones analíticas unidimensionales de Burgers y Richards bidimensionales. Se obtienen los mismos resultados para todos los solucionadores no lineales probados, pero se obtienen mejores tasas de convergencia con el método Newton Raphson en un esquema de doble iteración
