Chaotic Newton Iterative Method to Mechanism Synthesis Based on Chaotic Sequences Produced by Anti-control of Chaos in Induction Motor Motion

2009 ◽  
Author(s):  
Luo Youxin ◽  
Che Xiaoyi ◽  
Zeng Bin ◽  
Che Linxian
Keyword(s):  
Iterative Method ◽  
Induction Motor ◽  
Mechanism Synthesis ◽  
Control Of Chaos ◽  
Newton Iterative Method ◽  
Chaotic Sequences

Forward Displacement Analysis of Nine-Link Barranov Truss Based on Chaos Improved Newton Iterative Method

2011 ◽  
Vol 230-232 ◽  
pp. 743-748
Author(s):  
You Xin Luo ◽  
Bin Zeng
Keyword(s):  
Iterative Method ◽  
Vector Method ◽  
Forward Displacement ◽  
Displacement Analysis ◽  
Real Solutions ◽  
Newton Iterative Method ◽  
Chaotic Sequences ◽  
Constrained Equations ◽  
New Type ◽  
Forward Displacement Analysis

The chaos improved Newton iterative method finding all real solutions of nonlinear equations was proposed and the forward displacement analysis on the 25th nine-link Barranov truss was completed. Four constrained equations were established by vector method with complex numbers according to four loops of the mechanism and four supplement equations were also established by increasing four variables and the relation of sine and cosine function. The established eight equations are that of forward displacement analysis of the mechanism. Combining improved Newton iterative method with chaotic sequences, chaos improved Newton iterative method based on utilizing new type chaos system introduced by Chen to obtain locate initial points to find all real solutions of the nonlinear questions was proposed. The numerical example was given. The result shows that all real solutions have been quickly obtained, and it proves the correctness and validity of the proposed method.

Two-Dimensional Hyper-Chaotic Mapping Interval Newton Iterative Method to Mechanism Synthesis

2011 ◽  
Vol 230-232 ◽  
pp. 764-768
Author(s):  
You Xin Luo ◽  
Bin Zeng
Keyword(s):  
Iterative Method ◽  
Discrete Systems ◽  
Initial Guess ◽  
Two Dimensional ◽  
Mechanism Synthesis ◽  
Krawczyk Operator ◽  
Chaotic Mapping ◽  
Newton Iterative Method ◽  
Approximate Synthesis ◽  
Chaos Sequences

Mechanism synthesis questions can be transformed into nonlinear equations to be found. Interval Newton iterative method is an important technique to one dimensional and multidimensional variables and iterative process exhibits sensitive dependence on initial guess point. The characteristic of hyper-chaotic sequences produced by two dimensional hyper-chaotic discrete systems was analyzed. Making use of the advantage of giving rigorous bounds for the exact solution, for the first time, combining hyper-chaos sequences and interval Newton iteration with Krawczyk operator, a new method to find all solutions was proposed. The numerical examples in linkage synthesis and approximate synthesis show that the method is correct and effective.

scholarly journals Two solutions to Kirchhoff-type fourth-order implusive elastic beam equations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Jian Liu ◽  
Wenguang Yu
Keyword(s):  
Iterative Method ◽  
Variational Methods ◽  
Critical Point ◽  
Fourth Order ◽  
Elastic Beam ◽  
Kirchhoff Type ◽  
Newton Iterative Method ◽  
Beam Equations ◽  
Critical Point Theorems ◽  
Elastic Beam Equations

AbstractIn this paper, the existence of two solutions for superlinear fourth-order impulsive elastic beam equations is obtained. We get two theorems via variational methods and corresponding two-critical-point theorems. Combining with the Newton-iterative method, an example is presented to illustrate the value of the obtained theorems.

Forward Displacement Analysis of Nine-Link Barranov Truss Based on Anti-Control of Chaos Newton Downhill Method

2011 ◽  
Vol 230-232 ◽  
pp. 749-753
Author(s):  
You Xin Luo ◽  
Ying Yang
Keyword(s):  
Body Motion ◽  
Control Of Chaos ◽  
Vector Method ◽  
Forward Displacement ◽  
Displacement Analysis ◽  
Real Solutions ◽  
Chaotic Sequences ◽  
Motion System ◽  
Constrained Equations ◽  
Forward Displacement Analysis

The anti-control of chaos Newton downhill method finding all real solutions of nonlinear equations was proposed and the forward displacement analysis on the 25th nine-link Barranov truss was completed. Four constrained equations were established by vector method with complex numbers according to four loops of the mechanism and four supplement equations were also established by increasing four variables and the relation of sine and cosine function. The established eight equations are that of forward displacement analysis of the mechanism. Combining Newton downhill method with chaotic sequences, anti-control of chaos Newton downhill method based on utilizing anti-control of chaos in body motion system to obtain locate initial points to find all real solutions of the nonlinear questions was proposed. The numerical example was given.The result shows that all real solutions have been quickly obtained, and it proves the correctness and validity of the proposed method.

Research on Newton Iterative Method and its Application in Locating Problem of Cameras

2010 ◽  
Vol 108-111 ◽  
pp. 112-116
Author(s):  
Ai Min Yang ◽  
Jin Cai Chang ◽  
Shao Hong Yan
Keyword(s):  
Iterative Method ◽  
Plane Surface ◽  
Target Surface ◽  
Newton Iterative Method ◽  
Limited Condition ◽  
Surface Length

According to the imagery coordinate’s mapping relation between the three points’(A,C,E) geometric limited condition on target surface ( length, perpendicular) and the image’s coordinate on the imagery plane surface to construct non- lineable equation models, we make use of the method of abstracting the center of a circle to get the coordinates of the three points 、 、 .In order to improve the precision and decrease the quantity of operation, we take the accelerateNewton Newton iterative method to evaluate the original numerical value by adding its repeating times to increase the precision of model, then to solve out the numerical value of coordinates of the three points A,C,E on the target’s surface, on the basis of this numerical value, we can fix the solution of the target’s surface’s equation. Try to assure the precision of the constructed model through these erroneous values, meanwhile, to make out the concrete analysis about the model’s stability.

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