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2020, vol. 10, br. 1, str. 51-56
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Analysis of geodesics on different surfaces
(naslov ne postoji na srpskom)
Univerzitet u Prištini sa privremenim sedištem u Kosovskoj Mitrovici, Prirodno-matematički fakultet, Srbija
e-adresa: [email protected]
Projekat: Problemi Nelinearne analize, Teorije operatora, Topologije i primene (MPNTR - 174025)
Sažetak
(ne postoji na srpskom)
It is widely known that some surfaces contain special curves as a geodesics, while a lots of geodesics on surface have complicated shapes. Goal of this research is to find on what surfaces are u and v-parameter curves geodesics. Developable surfaces that contain a given plane curve as a geodesic are studied in the article, whereas the plane curve is also an initial u-parameter curve on that surface. Parametric equations of the minimal surfaces that contain an epicycloid as a geodesic are also given. Visualization of geodesics was done in Mathematica.
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Reference
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Abbena, E., S.S., G.A. (2006) Modern differential geometry of curves and surfaces with Mathematica. Boca Raton: CRC - Chapman and Hall
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Abdel-All, N.H., Abdel-Galil, E.I. (2013) Numerical treatment of geodesic differential equations on a surface in R^3. International Mathematical Forum, 8: 15-29
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Khuangsatung, W.C.P. (2012) Some geodesics in open surfaces classified by Clairauts relation. Engineering and Technology, 6(9): 1360-1364, World Academy of Science
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Lewis, J. (2002) Geodesics using Mathematica. Rose-Hulman Undergraduate Mathematics Journal, 3(1)
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