The University Thought - Publication in Natural Sciences
•01 Apr 2024
Analysis of geodesics on different surfaces
Maksimović, Miroslav • Jovanović, Tanja • Ljajko, Eugen • Ivanović, Milica
Abstract
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.
Funding
The first author was supported by the research project 174025 of the Serbian Ministry of Science.
Author: Maksimović, Miroslav • Jovanović, Tanja • Ljajko, Eugen • Ivanović, Milica
Issue: 1
Pages: 51-
56
doi: https://doi.org/10.5937/univtho10-20589
M kategorija: M53
Vrsta rada:clanak u casopisu
Funding: The first author was supported by the research project 174025 of the Serbian Ministry of Science.
Abstract
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.