Application of singular matrix beams in the symmetrical problem of definition of eigenvalues
The generalized problem of eigenvalue and vectors for singular matrix beams is central in the class of problems of rational construction of computed spectral models of complex modular systems. Solving this problem provides an opportunity to solve these problems, what determined the relevance of this...
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Institut za istrazivanja i projektovanja u privredi
2018-01-01
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doaj-9c80e8a468af4766939e5ce1fca51b182021-04-02T12:39:03ZengInstitut za istrazivanja i projektovanja u privrediIstrazivanja i projektovanja za privredu1451-41171821-31972018-01-011622812911451-41171802281SApplication of singular matrix beams in the symmetrical problem of definition of eigenvaluesSemenova Elena0Ivakin Yan1Frolova Elena2Fomina Alena3Smirnova Maria4Saint-Petersburg State University of Aerospace Instrumentation, Saint-Petersburg, Russian FederationSaint-Petersburg State University of Aerospace Instrumentation, Saint-Petersburg, Russian FederationSaint-Petersburg State University of Aerospace Instrumentation, Saint-Petersburg, Russian FederationCentral Research Institute of Economy, Management and Information Systems Electronics, Russian FederationSaint-Petersburg State University of Aerospace Instrumentation, Saint-Petersburg, Russian FederationThe generalized problem of eigenvalue and vectors for singular matrix beams is central in the class of problems of rational construction of computed spectral models of complex modular systems. Solving this problem provides an opportunity to solve these problems, what determined the relevance of this work. The design calculations of complex modular-modular systems have a multivariate character for ensuring their optimal characteristics due to variation within the permissible limits of the elastic-inertial parameters. In the general case such calculations acquire the character of structural-parametric synthesis, when the varied space is supplemented by corrective dynamic devices. The purpose of this article was to provide basic methods for carrying out these calculations. The approach based on the singular decomposition of characteristic matrices was taken as the basis of the research in this paper. This allowed the authors to propose a set of methods for solving this problem, adaptively taking into account the specificity of the available input data. The theoretical significance of the work lies in the development of the modern mathematical and algorithmic apparatus of singular matrix beams, and practical in developing a scientific and methodological basis for solving a corresponding class of applied problems of the dynamics of mechanical and electromechanical systems, for equivalent mathematical and simulation modeling of systems of this class.https://scindeks-clanci.ceon.rs/data/pdf/1451-4117/2018/1451-41171802281S.pdfmatrixmatrix beameigenvalue problemspec-central equationcharacteristic matrixcongruencedichotomycalculator |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Semenova Elena Ivakin Yan Frolova Elena Fomina Alena Smirnova Maria |
spellingShingle |
Semenova Elena Ivakin Yan Frolova Elena Fomina Alena Smirnova Maria Application of singular matrix beams in the symmetrical problem of definition of eigenvalues Istrazivanja i projektovanja za privredu matrix matrix beam eigenvalue problem spec-central equation characteristic matrix congruence dichotomy calculator |
author_facet |
Semenova Elena Ivakin Yan Frolova Elena Fomina Alena Smirnova Maria |
author_sort |
Semenova Elena |
title |
Application of singular matrix beams in the symmetrical problem of definition of eigenvalues |
title_short |
Application of singular matrix beams in the symmetrical problem of definition of eigenvalues |
title_full |
Application of singular matrix beams in the symmetrical problem of definition of eigenvalues |
title_fullStr |
Application of singular matrix beams in the symmetrical problem of definition of eigenvalues |
title_full_unstemmed |
Application of singular matrix beams in the symmetrical problem of definition of eigenvalues |
title_sort |
application of singular matrix beams in the symmetrical problem of definition of eigenvalues |
publisher |
Institut za istrazivanja i projektovanja u privredi |
series |
Istrazivanja i projektovanja za privredu |
issn |
1451-4117 1821-3197 |
publishDate |
2018-01-01 |
description |
The generalized problem of eigenvalue and vectors for singular matrix beams is central in the class of problems of rational construction of computed spectral models of complex modular systems. Solving this problem provides an opportunity to solve these problems, what determined the relevance of this work. The design calculations of complex modular-modular systems have a multivariate character for ensuring their optimal characteristics due to variation within the permissible limits of the elastic-inertial parameters. In the general case such calculations acquire the character of structural-parametric synthesis, when the varied space is supplemented by corrective dynamic devices. The purpose of this article was to provide basic methods for carrying out these calculations. The approach based on the singular decomposition of characteristic matrices was taken as the basis of the research in this paper. This allowed the authors to propose a set of methods for solving this problem, adaptively taking into account the specificity of the available input data. The theoretical significance of the work lies in the development of the modern mathematical and algorithmic apparatus of singular matrix beams, and practical in developing a scientific and methodological basis for solving a corresponding class of applied problems of the dynamics of mechanical and electromechanical systems, for equivalent mathematical and simulation modeling of systems of this class. |
topic |
matrix matrix beam eigenvalue problem spec-central equation characteristic matrix congruence dichotomy calculator |
url |
https://scindeks-clanci.ceon.rs/data/pdf/1451-4117/2018/1451-41171802281S.pdf |
work_keys_str_mv |
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