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master's thesis
Poyntingov teorem iz Hamiltonovog načela i prvog Noetherinog teorema
Split: University of Split, Faculty of Science, 2023. urn:nbn:hr:166:479464
Šesnić, Anamarija
University of Split
Faculty of Science
Department of Physics

Institutional repository: Repository of Faculty of Science

Cite this document

Šesnić, A. (2023). Poyntingov teorem iz Hamiltonovog načela i prvog Noetherinog teorema (Master's thesis). Split: University of Split, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:166:479464

Šesnić, Anamarija. "Poyntingov teorem iz Hamiltonovog načela i prvog Noetherinog teorema." Master's thesis, University of Split, Faculty of Science, 2023. https://urn.nsk.hr/urn:nbn:hr:166:479464

Šesnić, Anamarija. "Poyntingov teorem iz Hamiltonovog načela i prvog Noetherinog teorema." Master's thesis, University of Split, Faculty of Science, 2023. https://urn.nsk.hr/urn:nbn:hr:166:479464

Šesnić, A. (2023). 'Poyntingov teorem iz Hamiltonovog načela i prvog Noetherinog teorema', Master's thesis, University of Split, Faculty of Science, accessed 14 November 2024, https://urn.nsk.hr/urn:nbn:hr:166:479464

Šesnić A. Poyntingov teorem iz Hamiltonovog načela i prvog Noetherinog teorema [Master's thesis]. Split: University of Split, Faculty of Science; 2023 [cited 2024 November 14] Available at: https://urn.nsk.hr/urn:nbn:hr:166:479464

A. Šesnić, "Poyntingov teorem iz Hamiltonovog načela i prvog Noetherinog teorema", Master's thesis, University of Split, Faculty of Science, Split, 2023. Available at: https://urn.nsk.hr/urn:nbn:hr:166:479464

Metadata
TitlePoyntingov teorem iz Hamiltonovog načela i prvog Noetherinog teorema
Title (english)Poynting's theorem from Hamilton's principle and Noether's first theorem
AuthorAnamarija Šesnić
MentorDragan Poljak (mentor)
Committee memberDragan Poljak (predsjednik povjerenstva)
Committee memberPetar Stipanović (član povjerenstva)
Committee memberMarko Kovač (član povjerenstva)
GranterUniversity of Split
Faculty of Science
(Department of Physics)
Split
Defense date and country2023-07-14, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Physics
Abstract
Poyntingov teorem kao zakon očuvanja energije jedan je od osnovnih zakona u klasičnoj elektrodinamici. S druge strane, varijacijska načela postala su temeljni koncept za izgradnju modernih teorija u fizici. Stoga je zanimljivo istražiti kako Poyntingov teorem možemo izvesti iz prvih principa, točnije Hamiltonovog varijacijskog načela. Hamiltonovo načelo kaže da se fizički sustav ponaša tako da njegovo djelovanje bude stacionarno. Uvriježena je spoznaja u fizici da su zakoni očuvanja povezani sa simetrijama danog sustava. Tu vezu omogućuje prvi Noetherin teorem. Njegovu primjenu na klasičnu elektrodinamiku provodimo po Bessel-Hagenovoj metodi koja se u literaturi rijetko susreće. Posredovanjem prvog Noetherinog teorema i primjenom Hamiltonovog načela dosljedno stižemo do Poyntingovog teorema kada u prostoru nema naboja. Kod izvoda Poyntingovog teorema s izvorima pak uočavamo nedosljednosti koje upućuju na daljnje istraživanje problema, što ostavljamo za budući rad.
Abstract (english)
Poynting’s theorem is one of the fundamental laws in the theory of classical electrodynamics as a law of conservation of energy. On the other hand, variational principles have become a cornerstone of modern physical theories. It is therefore interesting to consider how Poynting’s theorem follows from first principles, Hamilton’s variational principle in particular. Hamilton’s principle states that a physical system behaves in such a way that makes action stationary. Furthermore, it is well established in physics that the conservation laws are related to the symmetries of a physical system, which is a consequence of Noether’s first theorem. We apply it to classical electrodynamics using the Bessel-Hagen method, which is rarely found in the literature. We show that a conjunction of Noether’s first theorem and Hamilton’s principle paves a consistent way of obtaining Poynting’s theorem in the case of no charge in the observed region. Derivation of Poynting’s theorem with sources, however, contains inconsistencies that point to further investigation of the problem, which is left for the future work.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:166:479464
Study programmeTitle: Physics; specializations in: major in teaching, major in Astrophysics, major in Biophysics, major in Enviromental physics, major in Computational physics, major in Astrophysics and physics of elemental particles
Course: major in Computational physics
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra fizike (magistar/magistra fizike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence Attribution-NoDerivatives 4.0 International (CC BY-ND 4.0) icon
Created on2023-07-17 09:08:15