{"title":"Chains of rigid bodies and their numerical simulation by local frame methods","authors":"N. Sætran, A. Zanna","doi":"10.3934/jcd.2019021","DOIUrl":null,"url":null,"abstract":"We consider the dynamics and numerical simulation of systems of linked rigid bodies (chains). We describe the system using the moving frame method approach of [ 18 ]. In this framework, the dynamics of the \\begin{document}$ j $\\end{document} th body is described in a frame relative to the \\begin{document}$ (j-1) $\\end{document} th one. Starting from the Lagrangian formulation of the system on \\begin{document}$ {{\\rm{SO}}}(3)^{N} $\\end{document} , the final dynamic formulation is obtained by variational calculus on Lie groups. The obtained system is solved by using unit quaternions to represent rotations and numerical methods preserving quadratic integrals.","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3934/jcd.2019021","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 1
Abstract
We consider the dynamics and numerical simulation of systems of linked rigid bodies (chains). We describe the system using the moving frame method approach of [ 18 ]. In this framework, the dynamics of the \begin{document}$ j $\end{document} th body is described in a frame relative to the \begin{document}$ (j-1) $\end{document} th one. Starting from the Lagrangian formulation of the system on \begin{document}$ {{\rm{SO}}}(3)^{N} $\end{document} , the final dynamic formulation is obtained by variational calculus on Lie groups. The obtained system is solved by using unit quaternions to represent rotations and numerical methods preserving quadratic integrals.
We consider the dynamics and numerical simulation of systems of linked rigid bodies (chains). We describe the system using the moving frame method approach of [ 18 ]. In this framework, the dynamics of the \begin{document}$ j $\end{document} th body is described in a frame relative to the \begin{document}$ (j-1) $\end{document} th one. Starting from the Lagrangian formulation of the system on \begin{document}$ {{\rm{SO}}}(3)^{N} $\end{document} , the final dynamic formulation is obtained by variational calculus on Lie groups. The obtained system is solved by using unit quaternions to represent rotations and numerical methods preserving quadratic integrals.
期刊介绍：
Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance.
Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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