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undergraduate thesis
Frenetov trobrid krivulje
2021. urn:nbn:hr:126:277238
Cvijetović, Anđela
Josip Juraj Strossmayer University of Osijek
Department of Mathematics

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Cvijetović, A. (2021). Frenetov trobrid krivulje (Undergraduate thesis). Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:277238

Cvijetović, Anđela. "Frenetov trobrid krivulje." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2021. https://urn.nsk.hr/urn:nbn:hr:126:277238

Cvijetović, Anđela. "Frenetov trobrid krivulje." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2021. https://urn.nsk.hr/urn:nbn:hr:126:277238

Cvijetović, A. (2021). 'Frenetov trobrid krivulje', Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 22 December 2024, https://urn.nsk.hr/urn:nbn:hr:126:277238

Cvijetović A. Frenetov trobrid krivulje [Undergraduate thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2021 [cited 2024 December 22] Available at: https://urn.nsk.hr/urn:nbn:hr:126:277238

A. Cvijetović, "Frenetov trobrid krivulje", Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2021. Available at: https://urn.nsk.hr/urn:nbn:hr:126:277238

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Metadata
TitleFrenetov trobrid krivulje
Title (english)Frenet Frame of a Curve
AuthorAnđela Cvijetović
MentorLjiljana Primorac Gajčić (mentor)
GranterJosip Juraj Strossmayer University of Osijek
Department of Mathematics
Osijek
Defense date and country2021-09-03, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Geometry and Topology
Abstract
U ovom radu, bavit ćemo se Frenetovim trobridom krivulje \(c: I \rightarrow \mathbb{R}^{^{3}}, \mathbb{I}\subseteq \mathbb{R}\) koji predstavlja desnu ortonormiranu bazu od \(\mathbb{R}_{c(t)}^{3}\), tj. prostora svih vektora u točki c(t), t ∈ I. Najprije ćemo navesti teoriju linearne algebre koju ćemo koristiti kroz rad. Uvest ćemo neke važne pojmove u diferencijalnoj geometriji, poput regularnosti krivulje, duljine luka krivulje, reparametrizacije, zakrivljenosti i torzije. Nakon definicije i osnovnih svojstava Frenetovog trobrida krivulje, navest ćemo Frenetove formule koje povezuju vektorska polja Frenetovog trobrida s njihovim derivacijama. Kroz nekoliko primjera, vidjet ćemo primjenu formula za zakrivljenost i torziju krivulje te odrediti Frenetov trobrid nekih krivulja.
Abstract (english)
In this work, we will consider Frenet frame of a curve \(c: I \rightarrow \mathbb{R}^{^{3}}, I \subseteq \mathbb{R}\), which represents right orthonormal base of \(\mathbb{R}_{c(t)}^{3}\) , space of all vectors in a point c(t), t ∈ I. First of all, we are going to state theory of linear algebra that will be used throughout the work. We will introduce some important concepts in differential geometry, such as regular curve, arc length, reparametrization of a curve, curvature and torsion of a curve. After definition and basic properties of Frenet frame, we are going to list Frenet formulas, which connect vector fields of the Frenet frame with their derivations. Throughout few examples, we will see the application of formulas for curvature and torsion and also determine Frenet frame of some curves
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:277238
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
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Created on2021-10-11 06:43:52