Model of Sensitivity to the Initial Conditions of the Equations of Motion in the Electric Fieldn

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dc.citation.epage41
dc.citation.issue1
dc.citation.journalTitleОбчислювальні проблеми електротехніки
dc.citation.spage36
dc.citation.volume14
dc.contributor.affiliationНаціональний університет “Львівська політехніка”
dc.contributor.affiliationLviv Polytechnic National University
dc.contributor.authorЧабан, Василь
dc.contributor.authorTchaban, Vasil
dc.coverage.placenameЛьвів
dc.coverage.placenameLviv
dc.date.accessioned2025-11-04T10:18:09Z
dc.date.created2024-02-27
dc.date.issued2024-02-27
dc.description.abstractA numerical method for calculating steady periodic processes of nonlinear differential equations of motion in an electric field is proposed based on their integration under initial conditions that exclude transient reaction. The calculation of such initial conditions is based on Newton's iterative formula. At each iteration, together with the basic equations of motion, the corresponding equations of the first variation are integrated over the periodicity time interval, which represent a model of sensitivity to the initial conditions, In addition, the number of unknown variational equations has been reduced, which makes it possible to lower their order, and, at the same time, the order of the monodromy matrix. All this contributes to the simplification of the relevant computational algorithms and computer programs. The method takes into account the finite rate of electric field propagation.
dc.format.extent36-41
dc.format.pages6
dc.identifier.citationTchaban V. Model of Sensitivity to the Initial Conditions of the Equations of Motion in the Electric Fieldn / Vasil Tchaban // Computational Problems of Electrical Engineering. — Lviv : Lviv Politechnic Publishing House, 2024. — Vol 14. — No 1. — P. 36–41.
dc.identifier.citationenTchaban V. Model of Sensitivity to the Initial Conditions of the Equations of Motion in the Electric Fieldn / Vasil Tchaban // Computational Problems of Electrical Engineering. — Lviv : Lviv Politechnic Publishing House, 2024. — Vol 14. — No 1. — P. 36–41.
dc.identifier.doidoi.org/10.23939/jcpee2024.01.036
dc.identifier.urihttps://ena.lpnu.ua/handle/ntb/117212
dc.language.isoen
dc.publisherВидавництво Львівської політехніки
dc.publisherLviv Politechnic Publishing House
dc.relation.ispartofОбчислювальні проблеми електротехніки, 1 (14), 2024
dc.relation.ispartofComputational Problems of Electrical Engineering, 1 (14), 2024
dc.relation.references[1] V. Tchaban, Electrogravity: movement in electric and gravitational field, Lviv: Space M, 2023, 160 p. (ISBN 978-617-8055-50-9).
dc.relation.references[2] Чабан В. Числові методи. Львів, 2001, 186 с.
dc.relation.references[3] V. Tchaban, Panta Rei (in Ukrainian). Lviv: Space M, p. 118, 2020, (ISBN 978-617-7746-60-6).
dc.relation.references[4] V.Tchaban, Movement in the gravitational and electric fields (in Ukrainian), Lviv: Space M, p. 140, 2021. ISBN 978-617-8055-01-1
dc.relation.references[5] V. Tchaban, “Electric intraction of electron-proton tandem”, Computational Problems of Electrical Engineering, vol. 11, no 2, pp. 38–42, 2021.
dc.relation.references[6] V. Tchaban, “Combined equations of electricity and gravity”, Technical news (Technical news), vol. 51, no 1, pp. 9–15, 2020 (in Ukrainian).
dc.relation.references[7] V. Tchaban, “Issue on Measuring the Light speed in Vacuum”, Measuring, Equipment and Metrology, vol. 82, no. 4, pp. 61–64, 2021. DOI: https://doi.org/10.23939/istcmtm2021.04.046.
dc.relation.references[8] V. Tchaban, “Radial Heliocentric Accelration of Spacecraft of Movement”, Modern Methods for the Development of Science, I Intern. Scientific and Practical Conference, Haifa, Izrael, pp. 330–334, January 09–11, 2023.
dc.relation.references[9] V. Chaban, “Substantiation of the anomalies of the measurement results for trajectories of gravitational maneuver of space vehicles”, Measuring, Equipment and Metrology, vol 85, no 1, pp. 5–9, 2024. (https://doi.org/10.23939/istcmtm2024.01.005).
dc.relation.references[10] V. Tchaban, “Theoretical justification of Faraday's experimental law”, Computational Problems of Electrical Engineering, vol. 12, no 1, pp. 31–34, 2023. (https://doi.org/10.23939/jcpee2023.01.031).
dc.relation.references[11] V. Chaban, Theoretical substantiation of the results of the laser location of the trajectory of the Moon moving away from the Earth.
dc.relation.references[12] V. Tchaban, Radial Componet of Vortex Ektctric Field Force. Computational Problems of Electrical Engineering, vol. 11, No. 1, 2021, pp. 32–35.
dc.relation.references[13] V. Tchaban, “Dynamic of Motion of Electron in Electrical Field”, Meassuring, Equipment and Metrology, vol 81, no. 2, pp. 39–42, 2020. (https://doi.org/10.23939/istcmtm2020.02.039).
dc.relation.referencesen[1] V. Tchaban, Electrogravity: movement in electric and gravitational field, Lviv: Space M, 2023, 160 p. (ISBN 978-617-8055-50-9).
dc.relation.referencesen[2] Chaban V. Chyslovi metody. Lviv, 2001, 186 p.
dc.relation.referencesen[3] V. Tchaban, Panta Rei (in Ukrainian). Lviv: Space M, p. 118, 2020, (ISBN 978-617-7746-60-6).
dc.relation.referencesen[4] V.Tchaban, Movement in the gravitational and electric fields (in Ukrainian), Lviv: Space M, p. 140, 2021. ISBN 978-617-8055-01-1
dc.relation.referencesen[5] V. Tchaban, "Electric intraction of electron-proton tandem", Computational Problems of Electrical Engineering, vol. 11, no 2, pp. 38–42, 2021.
dc.relation.referencesen[6] V. Tchaban, "Combined equations of electricity and gravity", Technical news (Technical news), vol. 51, no 1, pp. 9–15, 2020 (in Ukrainian).
dc.relation.referencesen[7] V. Tchaban, "Issue on Measuring the Light speed in Vacuum", Measuring, Equipment and Metrology, vol. 82, no. 4, pp. 61–64, 2021. DOI: https://doi.org/10.23939/istcmtm2021.04.046.
dc.relation.referencesen[8] V. Tchaban, "Radial Heliocentric Accelration of Spacecraft of Movement", Modern Methods for the Development of Science, I Intern. Scientific and Practical Conference, Haifa, Izrael, pp. 330–334, January 09–11, 2023.
dc.relation.referencesen[9] V. Chaban, "Substantiation of the anomalies of the measurement results for trajectories of gravitational maneuver of space vehicles", Measuring, Equipment and Metrology, vol 85, no 1, pp. 5–9, 2024. (https://doi.org/10.23939/istcmtm2024.01.005).
dc.relation.referencesen[10] V. Tchaban, "Theoretical justification of Faraday's experimental law", Computational Problems of Electrical Engineering, vol. 12, no 1, pp. 31–34, 2023. (https://doi.org/10.23939/jcpee2023.01.031).
dc.relation.referencesen[11] V. Chaban, Theoretical substantiation of the results of the laser location of the trajectory of the Moon moving away from the Earth.
dc.relation.referencesen[12] V. Tchaban, Radial Componet of Vortex Ektctric Field Force. Computational Problems of Electrical Engineering, vol. 11, No. 1, 2021, pp. 32–35.
dc.relation.referencesen[13] V. Tchaban, "Dynamic of Motion of Electron in Electrical Field", Meassuring, Equipment and Metrology, vol 81, no. 2, pp. 39–42, 2020. (https://doi.org/10.23939/istcmtm2020.02.039).
dc.relation.urihttps://doi.org/10.23939/istcmtm2021.04.046
dc.relation.urihttps://doi.org/10.23939/istcmtm2024.01.005
dc.relation.urihttps://doi.org/10.23939/jcpee2023.01.031
dc.relation.urihttps://doi.org/10.23939/istcmtm2020.02.039
dc.rights.holder© Національний університет “Львівська політехніка”, 2024
dc.subjectelectric field
dc.subjectnonlinear differential equations of motion
dc.subjectperiodic solutions
dc.subjectmodel of sensitivity to initial conditions
dc.subjectreduction of order of variational equations and monodromy matrix
dc.titleModel of Sensitivity to the Initial Conditions of the Equations of Motion in the Electric Fieldn
dc.title.alternativeМодель чутливости до початкових умов рівнянь руху в електричному полі
dc.typeArticle

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Computational Problems Of Electrical Engineering. – 2024. – Vol. 14, No. 1