Loss of power supply probability of stand-alone wind electric conversion systems: a closed form solution approach

1990 ◽  
Vol 5 (3) ◽  
pp. 445-452 ◽  
Author(s):  
I. Abouzahr ◽  
R. Ramakumar
Keyword(s):  
Closed Form ◽  
Power Supply ◽  
Closed Form Solution ◽  
Form Solution ◽  
Solution Approach

A Hybrid Approach to Solving the Position Equations for Planar Mechanisms

1995 ◽  
Vol 117 (4) ◽  
pp. 627-632 ◽  
Author(s):  
S. Bawab ◽  
G. L. Kinzel
Keyword(s):  
Closed Form ◽  
Hybrid Approach ◽  
Closed Form Solution ◽  
Iterative Solution ◽  
Form Solution ◽  
Planar Mechanisms ◽  
Solution Approach ◽  
Newton Raphson ◽  
Raphson Method ◽  
Straightforward Approach

In this paper, a straightforward approach is developed to solve the nonlinear position equations for a linkage when a closed-form solution to some of the equations can be obtained. This is done with the aid of dependency checking concepts that organizes a system 2n equations and 2n unknowns (variables) into smaller sets of equations. When a set of two equations and two unknowns is obtained, the variables are analyzed using a closed-form (non-iterative) solution approach. Otherwise, an iterative approach such as the Newton-Raphson method is used for the analysis.

On a Closed-Form Solution of Prandtl's System of Equations

2013 ◽  
Vol 40 (2) ◽  
pp. 106-114
Author(s):  
J. Venetis ◽  
Aimilios (Preferred name Emilios) Sideridis
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
System Of Equations

scholarly journals A Closed-Form Solution to Planar Feature-Based Registration of LiDAR Point Clouds

2021 ◽  
Vol 10 (7) ◽  
pp. 435
Author(s):  
Yongbo Wang ◽  
Nanshan Zheng ◽  
Zhengfu Bian
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Simulated Data ◽  
Real Data ◽  
Point Clouds ◽  
Form Solution ◽  
Spatial Transformation ◽  
Dual Quaternions ◽  
Feature Based ◽  
Planar Feature

Since pairwise registration is a necessary step for the seamless fusion of point clouds from neighboring stations, a closed-form solution to planar feature-based registration of LiDAR (Light Detection and Ranging) point clouds is proposed in this paper. Based on the Plücker coordinate-based representation of linear features in three-dimensional space, a quad tuple-based representation of planar features is introduced, which makes it possible to directly determine the difference between any two planar features. Dual quaternions are employed to represent spatial transformation and operations between dual quaternions and the quad tuple-based representation of planar features are given, with which an error norm is constructed. Based on L2-norm-minimization, detailed derivations of the proposed solution are explained step by step. Two experiments were designed in which simulated data and real data were both used to verify the correctness and the feasibility of the proposed solution. With the simulated data, the calculated registration results were consistent with the pre-established parameters, which verifies the correctness of the presented solution. With the real data, the calculated registration results were consistent with the results calculated by iterative methods. Conclusions can be drawn from the two experiments: (1) The proposed solution does not require any initial estimates of the unknown parameters in advance, which assures the stability and robustness of the solution; (2) Using dual quaternions to represent spatial transformation greatly reduces the additional constraints in the estimation process.

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