M. Maksimović, T. Jovanović, E. Ljajko, Milica Ivanović
{"title":"Analysis of geodesics on different surfaces","authors":"M. Maksimović, T. Jovanović, E. Ljajko, Milica Ivanović","doi":"10.5937/univtho10-20589","DOIUrl":null,"url":null,"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 uand vparameter 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.","PeriodicalId":22896,"journal":{"name":"The University Thought - Publication in Natural Sciences","volume":"25 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"The University Thought - Publication in Natural Sciences","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5937/univtho10-20589","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
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 uand vparameter 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.