Computation of Common Normal Between a Wheelset and Straight Rail at Singular Position

2014 ◽  
Author(s):  
Behrooz Fallahi ◽  
Arjun Kumar Perla ◽  
Andrew Behnke
Keyword(s):  
Coordinate System ◽  
Nonlinear Equations ◽  
Newton Method ◽  
Hybrid Procedure ◽  
Bisection Method ◽  
Parametric Equation ◽  
Wheel Surface ◽  
Special Position ◽  
The Common ◽  
Position And Orientation

Computation of common normal between a pair of wheel and rail surface is an important sub problem in railroad simulations. In this study, it is shown that there are special position and orientation of every wheelset that makes the governing equation for computation of the common normal degenerate. This condition leads to divergence of the Newton’s iterate. To develop a procedure that can successfully compute the common normal between a straight rail and a wheelset, first parametric equation for the rail and wheel surface in track coordinate system is developed. Then four nonlinear equations whose solution is location of common normal are constructed. Three of the equations are used to eliminate three unknown in fourth equation. The resulting equation has only one unknown. A hybrid procedure based on Newton method and bisection method is used to solve the roots of the last equation. The utility of this approach is demonstrated by reporting the common normal for a pair of wheel and rail surface at singular position.

scholarly journals Metode Iterasi Tiga Langkah untuk Menyelesaikan Persamaan NonLinear dengan Menggunakan Matlab

2019 ◽  
Vol 4 (2) ◽  
pp. 34
Author(s):  
Deasy Wahyuni ◽  
Elisawati Elisawati
Keyword(s):  
Numerical Simulations ◽  
Nonlinear Equations ◽  
Newton Method ◽  
Iteration Method ◽  
Newton's Method ◽  
Order Of Convergence ◽  
Higher Order ◽  
Convergence Order ◽  
Matlab Program ◽  
Analytical Results

Newton method is one of the most frequently used methods to find solutions to the roots of nonlinear equations. Along with the development of science, Newton's method has undergone various modifications. One of them is the hasanov method and the newton method variant (vmn), with a higher order of convergence. In this journal focuses on the three-step iteration method in which the order of convergence is higher than the three methods. To find the convergence order of the three-step iteration method requires a program that can support the analytical results of both methods. One of them using the help of the matlab program. Which will then be compared with numerical simulations also using the matlab program.  Keywords : newton method, newton method variant, Hasanov Method and order of convergence

An efficient fourth order weighted-Newton method for systems of nonlinear equations

2012 ◽  
Vol 62 (2) ◽  
pp. 307-323 ◽  
Author(s):  
Janak Raj Sharma ◽  
Rangan Kumar Guha ◽  
Rajni Sharma
Keyword(s):  
Nonlinear Equations ◽  
Newton Method ◽  
Fourth Order ◽  
Systems Of Nonlinear Equations

A Service Robot with Lightweight Arms and a Trinocular Vision Sensor

2010 ◽  
Vol 439-440 ◽  
pp. 396-400
Author(s):  
Xian Hua Li ◽  
Shi Li Tan ◽  
Wu Xin Huang
Keyword(s):  
Control System ◽  
Coordinate System ◽  
Inverse Kinematics ◽  
Robot Control ◽  
Service Robot ◽  
Algebraic Solution ◽  
Vision Sensor ◽  
Solution Methods ◽  
Space Coordinate ◽  
Position And Orientation

This paper describes a household service robot with two lightweight arms and a trinocular vision sensor. According to DH convention, the coordinate system of two arms is established, and position and orientation of the hand is computed. The inverse kinematics of the arm is solved with geometric and algebraic solution methods. By the trinocular vision sensor, robot can recognize the bottle and get its 3-D space coordinate. Through experiments, both correctness of the algorithm and stability of the robot control system are validated.

Interacting dipole pairs on a rotating sphere

2008 ◽  
Vol 464 (2094) ◽  
pp. 1525-1541 ◽  
Author(s):  
Paul K Newton ◽  
Houman Shokraneh
Keyword(s):  
Coordinate System ◽  
Long Range ◽  
Nonlinear Equations ◽  
Unit Sphere ◽  
Point Vortices ◽  
Geodesic Motion ◽  
Rotating Sphere ◽  
Long Range Interactions ◽  
Geodesic Paths ◽  
Exchange Scattering

The evolution, interaction and scattering of 2 N point vortices grouped into equal and opposite pairs ( N -dipoles) on a rotating unit sphere are studied. A new coordinate system made up of centres of vorticity and centroids associated with each dipole is introduced. With these coordinates, the nonlinear equations for an isolated dipole diagonalize and one directly obtains the equation for geodesic motion on the sphere for the dipole centroid. When two or more dipoles interact, the equations are viewed as an interacting billiard system on the sphere—charged billiards—with long-range interactions causing the centroid trajectories to deviate from their geodesic paths. Canonical interactions are studied both with and without rotation. For two dipoles, the four basic interactions are described as exchange-scattering , non-exchange-scattering , loop-scattering (head on) and loop-scattering (chasing) interactions. For three or more dipoles, one obtains a richer variety of interactions, although the interactions identified in the two-dipole case remain fundamental.

IMPLIED VOLATILITY FROM ASIAN OPTIONS VIA MONTE CARLO METHODS

2009 ◽  
Vol 12 (02) ◽  
pp. 153-178
Author(s):  
ZHAOJUN YANG ◽  
CHRISTIAN-OLIVER EWALD ◽  
YAJUN XIAO
Keyword(s):  
Monte Carlo ◽  
Nonlinear Equations ◽  
Newton Method ◽  
Monte Carlo Methods ◽  
Implied Volatility ◽  
Asian Options ◽  
Classical Approach ◽  
Fast Computation ◽  
Monte Carlo Techniques ◽  
Logarithmic Derivatives

We discuss how implied volatilities for OTC traded Asian options can be computed by combining Monte Carlo techniques with the Newton method in order to solve nonlinear equations. The method relies on accurate and fast computation of the corresponding vegas of the option. In order to achieve this we propose the use of logarithmic derivatives instead of the classical approach. Our simulations document that the proposed method shows far better results than the classical approach. Furthermore we demonstrate how numerical results can be improved by localization.

scholarly journals Numerical Solution of Nonlinear Equations in Maple

2021 ◽  
Vol 8 (4) ◽  
Author(s):  
Qani Yalda
Keyword(s):  
Numerical Methods ◽  
Numerical Solution ◽  
Numerical Method ◽  
Nonlinear Equations ◽  
Secant Method ◽  
Bisection Method ◽  
Real Roots ◽  
Newton Raphson ◽  
Root Analysis ◽  
Raphson Method

The main purpose of this paper is to obtain the real roots of an expression using the Numerical method, bisection method, Newton's method and secant method. Root analysis is calculated using specific, precise starting points and numerical methods and is represented by Maple. In this research, we used Maple software to analyze the roots of nonlinear equations by special methods, and by showing geometric diagrams, we examined the relevant examples. In this process, the Newton-Raphson method, the algorithm for root access, is fully illustrated by Maple. Also, the secant method and the bisection method were demonstrated by Maple by solving examples and drawing graphs related to each method.

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