scholarly journals Algebraic Techniques for Linear Equations over Quaternions and Split Quaternions: A Unified Approach in Quaternionic and Split Quaternionic Mechanics

2019 ◽  
Vol 07 (08) ◽  
pp. 1718-1731
Author(s):  
Gang Wang ◽  
Zhenwei Guo ◽  
Dong Zhang ◽  
Tongsong Jiang
Keyword(s):  
Linear Equations ◽  
Unified Approach ◽  
Split Quaternions

scholarly journals A Unified Approach to Nonlinear Dynamic Inversion Control with Parameter Determination by Eigenvalue Assignment

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
Yu-Chi Wang ◽  
Donglong Sheu ◽  
Chin-E Lin
Keyword(s):  
Nonlinear Dynamic ◽  
Feedback Linearization ◽  
Linear Equations ◽  
Parameter Determination ◽  
Dynamic Inversion ◽  
Unified Approach ◽  
Assignment Method ◽  
Modeling Uncertainties ◽  
Nonlinear Dynamic Inversion ◽  
Eigenvalue Assignment

This paper presents a unified approach to nonlinear dynamic inversion control algorithm with the parameters for desired dynamics determined by using an eigenvalue assignment method, which may be applied in a very straightforward and convenient way. By using this method, it is not necessary to transform the nonlinear equations into linear equations by feedback linearization before beginning control designs. The applications of this method are not limited to affine nonlinear control systems or limited to minimum phase problems if the eigenvalues of error dynamics are carefully assigned so that the desired dynamics is stable. The control design by using this method is shown to be robust to modeling uncertainties. To validate the theory, the design of a UAV control system is presented as an example. Numerical simulations show the performance of the design to be quite remarkable.

scholarly journals A Unified Approach: Split Quaternions with Quaternion Coefficients and Quaternions with Dual Coefficients

Mathematics ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 2149
Author(s):  
Emel Karaca ◽  
Fatih Yılmaz ◽  
Mustafa Çalışkan
Keyword(s):  
Unified Approach ◽  
Split Quaternions

This paper aims to present, in a unified manner, results which are valid on both split quaternions with quaternion coefficients and quaternions with dual coefficients, simultaneously, calling the attention to the main differences between these two quaternions. Taking into account some results obtained by Karaca, E. et al., 2020, each of these quaternions is studied and some important differences are remarked on.

Cramer’s rule over quaternions and split quaternions: A unified algebraic approach in quaternionic and split quaternionic mechanics

2020 ◽  
pp. 2150080
Author(s):  
Gang Wang ◽  
Dong Zhang ◽  
Zhenwei Guo ◽  
Tongsong Jiang
Keyword(s):  
Matrix Representation ◽  
Linear Equations ◽  
Algebraic Approach ◽  
Complex Matrix ◽  
Split Quaternions ◽  
Quaternion Matrices ◽  
Cramer’S Rule ◽  
Algebraic Technique

This paper aims to present, in a unified manner, Cramer’s rule which are valid on both the algebras of quaternions and split quaternions. This paper, introduces a concept of v-quaternion, studies Cramer’s rule for the system of v-quaternionic linear equations by means of a complex matrix representation of v-quaternion matrices, and gives an algebraic technique for solving the system of v-quaternionic linear equations. This paper also gives a unification of algebraic techniques for Cramer’s rule in quaternionic and split quaternionic mechanics.

Global steady state simulation of complex technological systems - an unified approach

1980 ◽  
Vol 45 (12) ◽  
pp. 3436-3459
Author(s):  
Josef Vrba
Keyword(s):  
Steady State ◽  
Linear Equations ◽  
Computational Algorithms ◽  
Algebraic Equations ◽  
Global Approach ◽  
Technological Systems ◽  
Unified Approach ◽  
Decomposition Level ◽  
Steady State Simulation

In general, mathematical models of steady state simulation schemas of complex technological processes are formed by sets of algebraic equations. The formal description of global approach to the solution of such sets is presented. The utilization of preliminary solution of linear equations of the set for its reduction and for the expression of dependency of the so-called eliminated variables on the remaining ones, as arguments of the reduced set, (i.e. the first decomposition level) is considered. The determination of disjoint subsystems of the reduced set (i.e. the subsets of nonlinear equations which may be solved serially and independently of each other in a sequence) and the determination of the hierarchy of their solution, when there are several such subsystems, is meant as the second decomposition level. The possibility of including of special models with particular computational algorithms in the equation-like model of complex system and the way of solution of such a problem with the mentioned two-level decomposition is also discussed. The including of both types of decomposition and the solution of the reduced set of equations in common computational block is dealt with.

A Unified Approach to Study the Thermal Dynamics in Multilongitudinal Mode Semiconductor Lasers

2001 ◽  
Vol 20 (2) ◽  
pp. 159-169 ◽  
Author(s):  
M. Ganesh Madhan ◽  
P. R. Vaya ◽  
N. Gunasekaran
Keyword(s):  
Semiconductor Lasers ◽  
Unified Approach ◽  
Thermal Dynamics

The influence of extrinsic motivation and work experience on employee performance (Case study in the Serang Baru Sub-district, Bekasi District)

2020 ◽  
Vol 5 (02) ◽  
pp. 167
Author(s):  
Nur’enny Nur’enny ◽  
Rahmat Hidayat
Keyword(s):  
Work Experience ◽  
Extrinsic Motivation ◽  
Employee Performance ◽  
Linear Equations ◽  
Test Reliability ◽  
Coefficient Of Determination ◽  
District Office ◽  
Normality Test ◽  
Observation Methods ◽  
Saturated Sample

This study aims to obtain information about extrinsic motivation and work experience and its effect on employee performance in the Serang Baru District Office. This study uses a saturated sample so that the population is the same as the sample of 80 employees, at the Serang Baru District Office. The method used is validation test, reliability test, then classical assumption test, which includes normality test and multicollinearity, as well as heteroscedasticity test, multiple linear analysis test, multiple linear equations, F test, coefficient of determination, and t test. The data of this research used observation methods and questionnaires distributed to 80 samples which were addressed to employees of the Serang Baru District Office. Based on the results of research and discussion, it can be concluded: 1) Extrinsic motivation does not affect employee performance because employees are willing to work more than expected regardless of extrinsic motivation or not. 2) Employee performance is strongly influenced by work experience. The more experience, they get while working, the more knowledge they will get. 3) Employee performance will be better with the support of experienced employees so as to increase the level of output produced.             Keywords: Employee Performance, Extrinsic Motivation, Work Experience

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