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HARMONICITY AND DIFFERENTIAL EQUATION OF INVOLUTE OF A CURVE IN E3

ABSTRACT
In this paper, we first give necessary conditions in which we can decide whether a given curve is biharmonic or 1-type harmonic and differential equations characterizing the regular curves. Then we research the Frenet formulas of involute of a unit speed curve by making use of the relations between the involute of a curve and the curve itself. In addition we apply these formulas to define the essential conditions by which one can determine whether the involute of a unit speed curve is biharmonic or 1-type harmonic and then we write differential equations characterizing the involute curve by means of Frenet apparatus of the unit speed curve. Finally we examined the helix as an example to illustrate how the given theorems work.
KEYWORDS
PAPER SUBMITTED: 2019-07-30
PAPER REVISED: 2019-09-20
PAPER ACCEPTED: 2019-09-29
PUBLISHED ONLINE: 2019-11-02
DOI REFERENCE: https://doi.org/10.2298/TSCI190730401C
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2019, VOLUME 23, ISSUE Supplement 6, PAGES [S2119 - S2125]
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© 2020 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence