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1
Content available The determinants of the block band matrices based on the n-dimensional Fourier equation
Biernat G., Lara-Dziembek S., Pawlak E.
Journal of Applied Mathematics and Computational Mechanics
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2015
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Vol. 14, nr 3
5--15
EN
This paper contains the method of calculating the determinant of the block band matrix on the example of n-dimensional Fourier equation using the FDM.
2
Content available Symmetric polynomials in the 3D Fourier equation
Biernat G., Lara-Dziembek S., Pawlak E.
Journal of Applied Mathematics and Computational Mechanics
|
2015
|
Vol. 14, nr 1
5--12
EN
The work is a continuation of the method of calculating the determinant of the block matrix in the three-dimensional case. In this article the symmetric polynomials are used.
3
Content available The n-dimensional Fourier equation with the Robin's boundary condition using the finite difference method
Biernat G., Lara-Dziembek S., Pawlak E.
Journal of Applied Mathematics and Computational Mechanics
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2014
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Vol. 13, nr 3
13--20
EN
The article is a continuation of the considerations on the three-dimensional Fourier equation supplemented by the third boundary condition (the Robin’s condition). The paper is based on the Finite Difference Method.
4
Content available The 3D Fourier equation with the Robin’s boundary condition using the finite difference method
Biernat G., Lara-Dziembek S., Pawlak E.
Journal of Applied Mathematics and Computational Mechanics
|
2014
|
Vol. 13, nr 1
5--11
EN
This article is a continuation of the discussion on the two-dimensional Fourier equation with Robin’s boundary condition. In the paper the Finite Difference Method is applied.
5
Content available Symmetric polynomials in the 2D Fourier equation
Biernat G., Lara-Dziembek S., Pawlak E.
Journal of Applied Mathematics and Computational Mechanics
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2014
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Vol. 13, nr 4
5--12
EN
The work is a continuation of the method of calculating the determinant of the block matrix in the two-dimensional case. In this paper we use the Finite Differences Method and the symmetric polynomials.
6
Content available The finite difference method in the 2D Fourier equation with Robin’s boundary condition
Biernat G., Lara-Dziembek S., Pawlak E.
Journal of Applied Mathematics and Computational Mechanics
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2013
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Vol. 12, nr 4
5--11
EN
This paper contains the application of the Finite Difference Method in the two-dimensional Fourier equation using Robin’s boundary condition (the third boundary condition).
7
Content available The determinants of the block band matrices based on the n-dimensional Fourier equation. Part 1
Biernat G., Lara-Dziembek S., Pawlak E.
Journal of Applied Mathematics and Computational Mechanics
|
2013
|
Vol. 12, nr 3
5--13
EN
This paper contains the method of calculating the determinant of the block band matrix on the example of n-dimensional Fourier equation using the Finite Difference Method.
8
Content available The determinants of the block band matrices based on the n-dimensional Fourier equation. Part 2
Biernat G., Lara-Dziembek S., Pawlak E.
Journal of Applied Mathematics and Computational Mechanics
|
2013
|
Vol. 12, nr 3
15--20
EN
This work is a continuation of the considerations concerning the determinants of the band block matrices on the example of the n-dimensional Fourier equation (work Part 1). The discussion will concern the special case called the three-dimensional Fourier equation.
9
Content available Using the block matrices in the modeling of driving and control system of hard disk drives
Trawiński T.
Prace Instytutu Elektrotechniki
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2011
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Z. 253
137-152
EN
In the article block matrix theory is employed to model of the branched kinematics chains. It allows for convenient construction of total dynamic matrix of complex branched kinematic system of head positioning system used in hard disk drives, with respect to enlargement of numbers of branches in kinematics chain. It allows giving the general expressions for individual matrix elements (in terms of basic kinematic parameters) before and after it inversion. In chapter 3 the block matrix inversion is discussed and finally in cheapter 4 the exemplary simulation results of time optimal control is presented.
PL
W artykule przedstawiono zastosowanie teorii macierzy blokowych do formułowania modeli matematycznych rozgałęzionych systemów pozycjonowania głowic pamięci masowych, z uwzględnieniem zwiększania liczby gałęzi łańcucha kinematycznego. Metoda pozwala na zapisanie ogólnej postaci na każdy element macierzy bezwładnościowych przed i po jej odwróceniu. W rozdziale 3 przedstawiono proces odwracania macierzy blokowej, a w rozdziale 4 przedstawiono przykładowe wyniki symulacyjne, potwierdzające prawidłowe sformułowanie modeli.
10
Content available remote Odwracanie macierzy o wybranych strukturach przy pomocy macierzy blokowych
Trawiński T.
Przegląd Elektrotechniczny
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2009
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R. 85, nr 6
98-101
PL
W niniejszym artykule przedstawiono metodę odwracania macierzy bezwładnościowych. Prezentowane macierze bezwładnościowe mają cechy symetrii charakterystyczne dla macierzy spotykanych w przetwornikach elektromechanicznych, bądź w robotyce w modelowaniu dynamiki manipulatorów robotów. Prezentowana metoda nadaje się do formułowania równań modeli matematycznych rozgałęzionych łańcuchów kinematycznych systemów pozycjonowania głowic pamięci masowych.
EN
In this article inversion method of inertial matrices is presented. Presented inertial matrices has similar structure to these which occur in electromechanical devices (such induction motors) or in robotics, in mathematical modeling of manipulators dynamics. Presented method is very helpful in mathematical equation formulation of branched positioning head system of mass storage devices.
11
Content available remote An extension of the Cayley-Hamilton theorem for a standard pair of block matrices
Kaczorek T.
Applied Mathematics and Computer Science
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1998
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Vol. 8, no 3
511-516
EN
The Cayley-Hamilton theorem is extended for a standard pair of matrices partitioned into blocks that commute in pairs. The Victoria theorem (Victoria, 1982) is a particular case for E = I of the extended Cayley-Hamilton theorem. The new theorem is illustrated by an example. Some remarks on extension of the theorem for non-square block matrices are also given.
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