ǂThe ǂtrue catenary

graduation thesis

Tjaša Hrovatič (Author), Andreas M. Hinz (Mentor), Uroš Milutinović (Co-mentor)

Abstract

In this thesis we introduce the problem of the ideal homogeneous hanging cable called the catenary. We observe the behaviour of the shape of the curve. Firstly, we solve the problem of the classical catenary on a flfat Earth, where the gravitational fifield is constant and perpendicular to the ground. Secondly, we focus on the true symmetric catenary in the central gravitational fifield, which comes from the -1/r potential. In both cases we use the method of calculus of variations for isoperimetric problems and in particular the Euler-Lagrange differential equation. Lastly, we explain the problem of the asymmetric case.

Keywords

Catenary;calculus of variations;Euler-Lagrange equation;curvature;potential energy;difffferential equation.;

Data

Language:	English
Year of publishing:	2013
Typology:	2.11 - Undergraduate Thesis
Organization:	UM FNM - Faculty of Natural Sciences and Mathematics
Publisher:	[T. Hrovatič]
UDC:	51(043.2)
COBISS:	20075784
Views:	1648
Downloads:	139
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	Slovenian
Secondary title:	Prava verižnica
Secondary abstract:	V tem diplomskem delu predstavimo problem idealne viseče homogene vrvi, ki jo imenujemo verižnica, in opazujemo obnašanje oblike te krivulje. Najprej rešimo problem klasične verižnice na ravni zemlji, kjer je gravitacijsko polje konstantno in pravokotno na podlago, nato pa se osredotočimo na pravo verižnico v središčnem gravitacijskem polju, ki je dobljeno iz -1/r potenciala. V obeh primerih uporabimo metodo variacijskega računa za izoperimetrični problem, še posebej Euler-Lagrangeevo diferencialno enačbo. Nazadnje razložimo tudi problem asimetrične verižnice.
Secondary keywords:	diplomska dela;verižnica;variacijski račun;Euler-Lagrangeeva enačba;diferencialne enačbe;ukrivljenost;matematika;
URN:	URN:SI:UM:
Type (COBISS):	Undergraduate thesis
Thesis comment:	Univ. v Mariboru, Fak. za naravoslovje in matematiko, Oddelek za matematiko in računalništvo
Pages:	71 f.
ID:	8727246