{"title":"一种利用双曲运动学求解曲面增长的新方法","authors":"Gül Tuğ, Zehra Özdemir","doi":"10.1002/mma.70020","DOIUrl":null,"url":null,"abstract":"<p>In the current work, we introduce the accretive growth of surfaces by using hyperbolical geometry. First, we describe hyperbolical kinematics along a generating curve to construct accretive surfaces having a hyperbolical cross-section. The obtained surfaces are not only the ones having hyperbolical cross-sections but also their material points follow a hyperbolic trajectory during the formation. Additionally, we explain the process by using hyperbolical split quaternions as an alternative perspective. This shows a remarkable simplicity in the construction of the mentioned surfaces. Then we investigate the connection between velocity and eccentricity of such surfaces together with a comparison to the circular motion. We present visualizations of several examples with the help of a programming language to support the theoretical results.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 16","pages":"15349-15363"},"PeriodicalIF":1.8000,"publicationDate":"2025-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mma.70020","citationCount":"0","resultStr":"{\"title\":\"A New Approach to the Accretive Growth of Surfaces Via Hyperbolical Kinematics\",\"authors\":\"Gül Tuğ, Zehra Özdemir\",\"doi\":\"10.1002/mma.70020\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>In the current work, we introduce the accretive growth of surfaces by using hyperbolical geometry. First, we describe hyperbolical kinematics along a generating curve to construct accretive surfaces having a hyperbolical cross-section. The obtained surfaces are not only the ones having hyperbolical cross-sections but also their material points follow a hyperbolic trajectory during the formation. Additionally, we explain the process by using hyperbolical split quaternions as an alternative perspective. This shows a remarkable simplicity in the construction of the mentioned surfaces. Then we investigate the connection between velocity and eccentricity of such surfaces together with a comparison to the circular motion. We present visualizations of several examples with the help of a programming language to support the theoretical results.</p>\",\"PeriodicalId\":49865,\"journal\":{\"name\":\"Mathematical Methods in the Applied Sciences\",\"volume\":\"48 16\",\"pages\":\"15349-15363\"},\"PeriodicalIF\":1.8000,\"publicationDate\":\"2025-08-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mma.70020\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematical Methods in the Applied Sciences\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1002/mma.70020\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Methods in the Applied Sciences","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/mma.70020","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
A New Approach to the Accretive Growth of Surfaces Via Hyperbolical Kinematics
In the current work, we introduce the accretive growth of surfaces by using hyperbolical geometry. First, we describe hyperbolical kinematics along a generating curve to construct accretive surfaces having a hyperbolical cross-section. The obtained surfaces are not only the ones having hyperbolical cross-sections but also their material points follow a hyperbolic trajectory during the formation. Additionally, we explain the process by using hyperbolical split quaternions as an alternative perspective. This shows a remarkable simplicity in the construction of the mentioned surfaces. Then we investigate the connection between velocity and eccentricity of such surfaces together with a comparison to the circular motion. We present visualizations of several examples with the help of a programming language to support the theoretical results.
期刊介绍：
Mathematical Methods in the Applied Sciences publishes papers dealing with new mathematical methods for the consideration of linear and non-linear, direct and inverse problems for physical relevant processes over time- and space- varying media under certain initial, boundary, transition conditions etc. Papers dealing with biomathematical content, population dynamics and network problems are most welcome.
Mathematical Methods in the Applied Sciences is an interdisciplinary journal: therefore, all manuscripts must be written to be accessible to a broad scientific but mathematically advanced audience. All papers must contain carefully written introduction and conclusion sections, which should include a clear exposition of the underlying scientific problem, a summary of the mathematical results and the tools used in deriving the results. Furthermore, the scientific importance of the manuscript and its conclusions should be made clear. Papers dealing with numerical processes or which contain only the application of well established methods will not be accepted.
Because of the broad scope of the journal, authors should minimize the use of technical jargon from their subfield in order to increase the accessibility of their paper and appeal to a wider readership. If technical terms are necessary, authors should define them clearly so that the main ideas are understandable also to readers not working in the same subfield.
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