Non-standard analysis in electrical engineering. Ideal DC inductive circuits with infinitesimal parameters of different orders
The analysis of DC circuits with ideal inductive elements using standard methods of theoretical electrical engineering is too difficult or even impossible, because when using them, it is often necessary to reveal type 00 uncertainties. In this regard, the article proposes to use not the usual mathe...
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| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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Academician Ye.A. Buketov Karaganda University
2025-06-01
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| Series: | Қарағанды университетінің хабаршысы. Физика сериясы |
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| Online Access: | https://phs.buketov.edu.kz/index.php/physics-vestnik/article/view/847 |
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| author | S. Katsyv V. Kukharchuk V. Madyarov V. Kucheruk P. Kulakov M. Нribov |
| author_facet | S. Katsyv V. Kukharchuk V. Madyarov V. Kucheruk P. Kulakov M. Нribov |
| author_sort | S. Katsyv |
| collection | DOAJ |
| description |
The analysis of DC circuits with ideal inductive elements using standard methods of theoretical electrical engineering
is too difficult or even impossible, because when using them, it is often necessary to reveal type
00 uncertainties. In this regard, the article proposes to use not the usual mathematical analysis, but a nonstandard
one, in which the frequency of the direct current is taken not as zero, but as an infinitesimal number
. In this case, the reactances of the inductive elements will be equal to L , and it becomes possible to apply
all standard methods of theoretical electrical engineering. The article considers examples of the analysis
of ideal DC inductive circuits, with particular attention paid to circuits whose calculation requires the use of
infinitesimal numbers for inhomogeneous parameters. In such cases, the order of these numbers is determined
based on individual considerations, and this is a non-standard task.
|
| format | Article |
| id | doaj-art-8b241e0d2f954a5c90a65e79c458a9dd |
| institution | OA Journals |
| issn | 2518-7198 2663-5089 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | Academician Ye.A. Buketov Karaganda University |
| record_format | Article |
| series | Қарағанды университетінің хабаршысы. Физика сериясы |
| spelling | doaj-art-8b241e0d2f954a5c90a65e79c458a9dd2025-08-20T02:07:57ZengAcademician Ye.A. Buketov Karaganda UniversityҚарағанды университетінің хабаршысы. Физика сериясы2518-71982663-50892025-06-0111830210.31489/2025ph2/87-96Non-standard analysis in electrical engineering. Ideal DC inductive circuits with infinitesimal parameters of different ordersS. KatsyvV. KukharchukV. MadyarovV. KucherukP. KulakovM. Нribov The analysis of DC circuits with ideal inductive elements using standard methods of theoretical electrical engineering is too difficult or even impossible, because when using them, it is often necessary to reveal type 00 uncertainties. In this regard, the article proposes to use not the usual mathematical analysis, but a nonstandard one, in which the frequency of the direct current is taken not as zero, but as an infinitesimal number . In this case, the reactances of the inductive elements will be equal to L , and it becomes possible to apply all standard methods of theoretical electrical engineering. The article considers examples of the analysis of ideal DC inductive circuits, with particular attention paid to circuits whose calculation requires the use of infinitesimal numbers for inhomogeneous parameters. In such cases, the order of these numbers is determined based on individual considerations, and this is a non-standard task. https://phs.buketov.edu.kz/index.php/physics-vestnik/article/view/847infinitesimal numberinfinitude,hyperreal numberunconventional numberideal reactive element |
| spellingShingle | S. Katsyv V. Kukharchuk V. Madyarov V. Kucheruk P. Kulakov M. Нribov Non-standard analysis in electrical engineering. Ideal DC inductive circuits with infinitesimal parameters of different orders Қарағанды университетінің хабаршысы. Физика сериясы infinitesimal number infinitude, hyperreal number unconventional number ideal reactive element |
| title | Non-standard analysis in electrical engineering. Ideal DC inductive circuits with infinitesimal parameters of different orders |
| title_full | Non-standard analysis in electrical engineering. Ideal DC inductive circuits with infinitesimal parameters of different orders |
| title_fullStr | Non-standard analysis in electrical engineering. Ideal DC inductive circuits with infinitesimal parameters of different orders |
| title_full_unstemmed | Non-standard analysis in electrical engineering. Ideal DC inductive circuits with infinitesimal parameters of different orders |
| title_short | Non-standard analysis in electrical engineering. Ideal DC inductive circuits with infinitesimal parameters of different orders |
| title_sort | non standard analysis in electrical engineering ideal dc inductive circuits with infinitesimal parameters of different orders |
| topic | infinitesimal number infinitude, hyperreal number unconventional number ideal reactive element |
| url | https://phs.buketov.edu.kz/index.php/physics-vestnik/article/view/847 |
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