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undergraduate thesis
Ravnoteža napete žice
2017. urn:nbn:hr:126:701478
Franjo, Martina
Josip Juraj Strossmayer University of Osijek
Department of Mathematics
Chair of Applied Mathematics and Computer Science
Applied Mathematics and Optimization Research Group

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Franjo, M. (2017). Ravnoteža napete žice (Undergraduate thesis). Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:701478

Franjo, Martina. "Ravnoteža napete žice." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2017. https://urn.nsk.hr/urn:nbn:hr:126:701478

Franjo, Martina. "Ravnoteža napete žice." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2017. https://urn.nsk.hr/urn:nbn:hr:126:701478

Franjo, M. (2017). 'Ravnoteža napete žice', Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 28 January 2025, https://urn.nsk.hr/urn:nbn:hr:126:701478

Franjo M. Ravnoteža napete žice [Undergraduate thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2017 [cited 2025 January 28] Available at: https://urn.nsk.hr/urn:nbn:hr:126:701478

M. Franjo, "Ravnoteža napete žice", Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2017. Available at: https://urn.nsk.hr/urn:nbn:hr:126:701478

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Metadata
TitleRavnoteža napete žice
Title (english)Equilibrium of Tension Wire
AuthorMartina Franjo
MentorKrešimir Burazin (mentor)
GranterJosip Juraj Strossmayer University of Osijek
Department of Mathematics
(Chair of Applied Mathematics and Computer Science)
(Applied Mathematics and Optimization Research Group)
Osijek
Defense date and country2017-09-29, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Applied Mathematics and Mathematical Modeling
Abstract
U ovom radu proučavat ćemo ravnotežu jednodimenzionalnih kontinuuma. Objasniti ćemo što je kontinuum, te na primjeru napete elastične žice prikazati izvod jednadžbe ravnoteže, koja je linearna diferencijalna jednadžba drugog reda. Izvesti ćemo i jednadžbu stacionarnog provodenja topline kroz štap te pokazati da je ona identična jednadžbi ravnoteže napete žice. Također, razmatrati ćemo ponašanje žice uz različite rubne uvjete. Iskazati ćemo i dokazati princip superpozicije koji nam je bitan za postupak homogenizacije rubnog problema i općenito kod odredivanja ravnotežnog položaja. Na kraju samog rada bavit ćemo se pitanjem jedinstvenosti rješenja te proći kroz slučajeve kad koeficijenti ne posjeduju dovoljnu glatkoću. Sve navedeno popraćeno je mnoštvom primjera i zadataka sa ilustracijama.
Abstract (english)
In this paper we will study equilibrium of one dimensional continuum. We will explain what continuum is and derive balance equation for elastic wire under tension, which is a second order linear differential equation. Additionally, we will derive equation of heat conduction through stick and show that this equation is identical to the balance equation of elastic wire. We will consider the behaviour of wire with respect to different boundary conditions. We will state and prove superposition principle which is very important for homogenzation of the boundary problem as well as for finding equilibrium position in general. At the end of this paper we will study uniqueness of the solution and go through cases when coefficients are not smooth enough. All mentioned results are complemented with a number of examples and illustrations.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:701478
Study programmeTitle: University undergraduate study programme in mathematics
Study programme type: university
Study level: undergraduate
Academic / professional title: sveučilišni/a prvostupnik/prvostupnica (baccalaureus/baccalaurea) matematike (sveučilišni/a prvostupnik/prvostupnica (baccalaureus/baccalaurea) matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2017-11-02 10:10:51