Applications of knot theory to the detection of heteroclinic connections between quasi-periodic orbits

<!doctype html> <html lang="en"> <head> <meta charset="UTF-8" /> <title>Applications of knot theory to the detection of heteroclinic connections between quasi-periodic orbits</title> <meta name="keywords" content="circular restricted three-body problem (CR3BP), quasi-periodic torus, heteroclinic connection, knot theory" /> <meta name="viewport" content="width=device-width, initial-scale=1, maximum-scale=1.0, user-scalable=0" /> <meta http-equiv="X-UA-Compatible" content="IE=edge,Chrome=1" /> <meta name="robots" content="noarchive" /> <meta property="og:title" content="Applications of knot theory to the detection of heteroclinic connections between quasi-periodic orbits" /> <meta property="og:type" content="Article" /> <meta property="og:url" content="https://www.sciopen.com/article/10.1007/s42064-024-0201-0" /> <meta property="og:site_name" content="SciOpen" /> <meta property="og:description" content="<p>Heteroclinic connections represent unique opportunities for spacecraft to transfer between isoenergetic libration point orbits for zero deterministic <inline-formula id="M1"> <math id="mathml_M1" display="inline" overflow="scroll"><mi mathvariant="normal">Δ</mi><mi>V</mi></math></inline-formula> expenditure. However, methods of detecting them can be limited, typically relying on human-in-the-loop or computationally intensive processes. In this paper we present a rapid and fully systematic method of detecting heteroclinic connections between quasi-periodic invariant tori by exploiting topological invariants found in knot theory. The approach is applied to the Earth–Moon, Sun–Earth, and Jupiter–Ganymede circular restricted three-body problems to demonstrate the robustness of this method in detecting heteroclinic connections between various quasi-periodic orbit families in restricted astrodynamical problems.</p>" /> <meta name="citation_doi" content="10.1007/s42064-024-0201-0" /> <meta name="dc.identifier" content="10.1007/s42064-024-0201-0" /> <meta name="citation_journal_title" content="Astrodynamics" /> <meta name="citation_title" content="Applications of knot theory to the detection of heteroclinic connections between quasi-periodic orbits" /> <meta content="circular restricted three-body problem (CR3BP)" name="citation_keywords" /><meta content="quasi-periodic torus" name="citation_keywords" /><meta content="heteroclinic connection" name="citation_keywords" /><meta content="knot theory" name="citation_keywords" /> <meta name="citation_volume" content="8" /> <meta name="citation_issue" content="4" /> <meta name="citation_firstpage" content="577" /> <meta name="citation_lastpage" content="595" /> <meta name="citation_publication_date" content="2024/12/1" /> <meta name="citation_online_date" content="2024/4/15" /> <meta name="citation_issn" content="2522-008X" /> <meta name="citation_language" content="en" /> <meta name="citation_author" content="Danny Owen" /> <meta name="citation_author_institution" content="Surrey Space Centre,University of Surrey, GU2 7XH," /> <meta name="citation_author" content="Nicola Baresi" /> <meta name="citation_author_institution" content="Surrey Space Centre,University of Surrey, GU2 7XH," /> <meta name="citation_abstract_html_url" content="https://www.sciopen.com/article/10.1007/s42064-024-0201-0" /> <meta name="citation_fulltext_html_url" content="https://www.sciopen.com/article/10.1007/s42064-024-0201-0" /> <meta name="citation_date" content="2024/12/01" /> <meta name="citation_pdf_url" content="https://sciopen.com/article_pdf/1840680512333123585.pdf" /> <meta name="citation_publisher" content="清华大学出版社" /> <meta name="citation_fulltext_world_readable" content="" /> <meta name="Description" content="<p>Heteroclinic connections represent unique opportunities for spacecraft to transfer between isoenergetic libration point orbits for zero deterministic <inline-formula id="M1"> <math id="mathml_M1" display="inline" overflow="scroll"><mi mathvariant="normal">Δ</mi><mi>V</mi></math></inline-formula> expenditure. However, methods of detecting them can be limited, typically relying on human-in-the-loop or computationally intensive processes. In this paper we present a rapid and fully systematic method of detecting heteroclinic connections between quasi-periodic invariant tori by exploiting topological invariants found in knot theory. The approach is applied to the Earth–Moon, Sun–Earth, and Jupiter–Ganymede circular restricted three-body problems to demonstrate the robustness of this method in detecting heteroclinic connections between various quasi-periodic orbit families in restricted astrodynamical problems.</p>" /> <meta name="article_references" content="Owen D, Baresi N. . Applications of knot theory to the detection of heteroclinic connections between quasi-periodic orbits. . <span style = 'font-style: italic;'>Astrodynamics</span>, . 2024, 8(4): 577-595. . https://doi.org/10.1007/s42064-024-0201-0" /> <script> var _hmt = _hmt || []; (function () { var hm = document.createElement('script'); hm.src = 'https://hm.baidu.com/hm.js?459d6fc0106b99052c6f753275cafeea'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(hm, s); })(); </script> <script> /** 数字分社统计 */ var _paq = (window._paq = window._paq || []); /* tracker methods like "setCustomDimension" should be called before "trackPageView" */ _paq.push(['trackPageView']); _paq.push(['enableLinkTracking']); (function () { var u = '//matomo.izhixue.cc/'; _paq.push(['setTrackerUrl', u + 'matomo.php']); _paq.push(['setSiteId', '3']); var d = document, g = d.createElement('script'), s = d.getElementsByTagName('script')[0]; g.async = true; g.src = u + 'matomo.js'; s.parentNode.insertBefore(g, s); })(); </script> <script async src="https://www.googletagmanager.com/gtag/js?id=G-5SWG8SFZJW"></script> <script> window.dataLayer = window.dataLayer || []; function gtag() { dataLayer.push(arguments); } gtag('js', new Date()); gtag('config', 'G-5SWG8SFZJW'); gtag('config', 'AW-10902746976'); </script> <link rel="icon" type="image/x-icon" href="/favicon.ico" /> <link rel="stylesheet" href="/assets/bootstrap/css/bootstrap.min.css" /> <link rel="stylesheet" href="/assets/bootstrap/css/bootstrap-theme.min.css" /> <link rel="stylesheet" type="text/css" href="/assets/css/main-0df796bfb407e1d169a43808ab1956d0.css" /> <link rel="stylesheet" type="text/css" href="" /> <link rel="stylesheet" href="/assets/css/yxshare-fef9fea08989beac7bbf5247cc50a495.css" /> <link rel="stylesheet" href="/assets/swiper/css/swiper.min.css" /> <link rel="stylesheet" href="/assets/viewer/viewer-c0ba7a3d525d8a4332954939894dbeab.css" /> <link rel="stylesheet" href="/assets/css/article-new-702ef1664c30d5c9d82fe28ad5760f1e.css" /> <script src="/assets/js/jquery.min.js"></script> <script type="text/x-mathjax-config"> MathJax.Hub.Config({ showProcessingMessages: false, messageStyle: 'none', }); </script> <script type="text/javascript" async src="https://wqketang.oss-cn-beijing.aliyuncs.com/ajax/libs/mathjax/2.7.7/MathJax.js?config=TeX-MML-AM_HTMLorMML"></script>  </head> <body> <div id="ai-chat"> <el-drawer class="ai-drawer-wrapper" custom-class="ai-drawer" title="标题" :before-close="aiDrawerClose" :visible.sync="aiDrawerShow" direction="rtl" :modal="false" :with-header="false" :append-to-body="true" :z-index="1001" > <div class="drawer-title"> <div class="left"> <img src="/assets/img/article/AM_Full.svg" /> <span>AI Chat Paper</span> </div> <div class="right"><i class="el-icon-close" @click="aiDrawerClose"></i></div> </div> <div class="drawer-body"> <div class="tips">Note: Please note that the following content is generated by AMiner AI. 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/> </svg> <span>Cite</span> <div class="download-boxs"> <a href="/article/download_ris?tag=2&id=1840680512333123585" target="_blank" class="item-box"> EndNote(RIS) </a> <a href="/article/download_ris?tag=3&id=1840680512333123585" target="_blank" class="item-box"> BibTeX </a> </div> </div>  <div class="v4-art-top-item" id="collection_not_1840680512333123585" onclick="openCheck("1840680512333123585")"> <svg class="vt-art-top-item-img" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" width="22" height="22" viewBox="0 0 200 200"> <image id="图层_1" data-name="图层 1" x="18" y="18" width="164" height="164" 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class="v4-outline-tables" v-if="tableMenuList.length>5"> <template slot="title" v-if="tableMenuList.length>5"> <span class="v4-show-hide-icon is-not-active" v-if="tableMenuList.length > 5">Show {{tableMenuList.length - 5}} more tables</span> <span class="v4-show-hide-icon is-active" v-if="tableMenuList.length > 5">Hide {{tableMenuList.length - 5}} tables</span> </template> <div class="v4-outline-table-item" v-for="(item, index) in tableMenuList" v-if="index > 4" @click="turnCurrentNode('content_' + item['key'])" v-html="item['label']"></div> </el-collapse-item> </el-collapse> </div> </div> <div class="v4-art-main-center"> <div class="art-html-center"> <div class="art-html-top"> <div class="v4-art-info">  <span>Research Article</span> <span style="font-family: auto" >|</span >   <span class="v4-art-info-oa">Open Access </span>  </div>  <h1 class="v4-ahc-title">Applications of knot theory to the detection of heteroclinic connections between quasi-periodic orbits</h1>  <div> <span class="art-authors" ><span><a href='/scholar/info?id=1840680514103119874'>Danny Owen</a></span><sup></sup ><span class="art-authors-email" style="padding-left: 3px" >(<a onclick="send_email("1840680514103119874","1840680512333123585")"> <el-tooltip popper-class="v4-el-tooltip" effect="dark" content="danny.owen@surrey.ac.uk" placement="top-start"> <img src="/assets/img/article/article-email.svg" style="width: 20px" /> </el-tooltip> </a >)</span ><span>, </span></span ><span class="art-authors" ><span><a href='/scholar/info?id=1678232200955846658'>Nicola Baresi</a></span><sup></sup ></span > </div> <div style="clear: both"></div> <div class="art-authors-unit art-authors-unit2"> <div class="art-authors-unit-inner art-authors-unit-inner2"> <div class="art-authors-unit-item"><addr-line>Surrey Space Centre, University of Surrey, Guildford, UK</addr-line></div> </div> </div> <div> <span class="art-authors art-authors-more art-authors-more2" onclick="showAuthUnit(3)"> Show Author Information <i class="el-icon-caret-bottom"></i> </span> <span class="art-authors art-authors-less art-authors-less2" style="display: none" onclick="showAuthUnit(4)"> Hide Author Information <i class="el-icon-caret-top"></i> </span> </div>  <div style="border-top: 1px solid #eef; margin-top: 20px; padding-bottom: 8px" ></div>  <div class="v4-art-content-p"> <h2></h2> </div>  <div class="v4-art-content-p v4-art-abstract" id="title_-2-1"> <h2>Graphical Abstract</h2> <div> <div id="v4_art_abstract_img"><img src="https://wqketang.oss-cn-beijing.aliyuncs.com/zip-unzip/zip-7679846b-b79a-4580-b2f0-b60ef155f0cf/astrodynamics-8-4-577/files/astrodynamics-8-4-577-FE1.jpg?Expires=1732391120&OSSAccessKeyId=STS.NSpqk4tC6Ru5rkHhuNvgjaw2W&Signature=fmdxzi9zujWeciz7IHDqkvRzAdY%3D&security-token=CAISywJ1q6Ft5B2yfSjIr5DFOtGAmZwX5bfecE35jHUbeuhGjrKZtTz2IHtKenhsBOsbtfk1mG5W5%2FgZlqJ9SptIAEfJa9d99MyFR9AuvtCT1fau5Jko1beHewHKeTOZsebWZ%2BLmNqC%2FHt6md1HDkAJq3LL%2Bbk%2FMdle5MJqP%2B%2FUFB5ZtKWveVzddA8pMLQZPsdITMWCrVcygKRn3mGHdfiEK00he8TouufTinpHMskGA1Aell7Mvyt6vcsT%2BXa5FJ4xiVtq55utye5fa3TRYgxowr%2Fwo0v0YpGya5YzHXwcPskvdKZbo78UqLQlla6w%2BGqFJqvPxr%2Fp8t%2Fx5fWJKAezhVgs8cVM8JOjIqKOscIsihmul4wzFcD1LXoQ6vH1ZZ5%2FAzVZaVWUEMpNqcRxTMldXaQqhSZT8m3upKXzOJeX7ls9%2Fv%2FV7p%2BNtHbjUTzDnGoABljLYqvsZH%2Fp3c6u5%2Fh4ZYrxRVq3ZNuFgFMmVvR2CogbYHFpJghu8z%2F7O5gd8c4FZsBbKYjwXQrg4p2p3vLN%2F3yaKBOhOAzsG6irYr%2BhBCVqQnaSsB79uIP4fdoDCX3VF5C5XeKQFVt9mQsRRryO0UVkpaC%2BJZfNNkFWId5FB6p0gAA%3D%3D"></div> </div> </div>  <div class="v4-art-content-p v4-art-abstract" id="title_-2"> <h2>Abstract</h2> <div><p>Heteroclinic connections represent unique opportunities for spacecraft to transfer between isoenergetic libration point orbits for zero deterministic <inline-formula id="M1"> <math id="mathml_M1" display="inline" overflow="scroll"><mi mathvariant="normal">Δ</mi><mi>V</mi></math></inline-formula> expenditure. However, methods of detecting them can be limited, typically relying on human-in-the-loop or computationally intensive processes. In this paper we present a rapid and fully systematic method of detecting heteroclinic connections between quasi-periodic invariant tori by exploiting topological invariants found in knot theory. The approach is applied to the Earth–Moon, Sun–Earth, and Jupiter–Ganymede circular restricted three-body problems to demonstrate the robustness of this method in detecting heteroclinic connections between various quasi-periodic orbit families in restricted astrodynamical problems.</p></div> </div>  <div class="v4-art-content-p" id="title_-3"> <h2>Keywords</h2> <div class="v4-art-keyword"> <a class="v4-art-keyword-item" onclick="jumpKeyword("circular restricted three-body problem (CR3BP)")" >circular restricted three-body problem (CR3BP)</a ><a class="v4-art-keyword-item" onclick="jumpKeyword("quasi-periodic torus")" >quasi-periodic torus</a ><a class="v4-art-keyword-item" onclick="jumpKeyword("heteroclinic connection")" >heteroclinic connection</a ><a class="v4-art-keyword-item" onclick="jumpKeyword("knot theory")" >knot theory</a > </div> </div>   <div id="title_-4" class="v4-art-content-p" style="display: none"></div> <div style="border-top: 1px solid #eef; margin-top: 20px"> <div id="article_no_data" style="padding-top: 30px; display: none"> <p>No abstract is available for this article. Click the button above to view the PDF directly.</p> </div>   <div id="insert_content"> <div id="insert_content_one"></div>  <div id="insert_content_two"></div>  <div class="v4-art-content-p" id="title_-12"> <h2>References</h2> <div id="article_references" style="overflow-x: auto; overflow-y: hidden"> <div class="v4-art-reference-item">  <div id="r_b1" class="v4-art-reference-item-index" onclick="findReferencesInContentById(this)" >[1]</div>    <div class="v4-art-reference-item-title"> <span>Koon, W. S., Lo, M. W., Marsden, J. E., Ross, S. D. The Genesis trajectory and heteroclinic connections. 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In: Proceedings of the 8th Western Computer Graphics Symposium, <strong>1997</strong>.</span> </div> </div> </div> </div> </div> </div> </div> </div> </div> <div class="v4-art-main-right"> <img class="v4-article-journal-img" src="/journal/get_journal_cover?flag=2&status=0&id=10.1007/s42064-024-0201-0" /> <a class="v4-article-journal-title" href="/journal/2522-008X">Astrodynamics</a> <div class="v4-art-main-right-content"> <a href="/journal/join_journal/stage_page?stage=5&id=1424923732016201729&issueIndex=1840680635293339650&issn=2522-008X" >Volume 8 Issue 4,</br>December 2024</a> </div> <div class="v4-art-main-right-content"> <span>Pages 577-595</span> </div> <div class="v4-art-main-right-content"> DOI: <a href="https://doi.org/10.1007/s42064-024-0201-0" target="_blank" style="word-break: break-all">10.1007/s42064-024-0201-0</a> </div> <div class="v4-art-main-right-title">Cite this article:</div> <div class="v4-art-main-right-content"> <span>Owen D, Baresi N. </span> <span>Applications of knot theory to the detection of heteroclinic connections between quasi-periodic orbits. </span> <span><span style = 'font-style: italic;'>Astrodynamics</span>, </span> <span> 2024, 8(4): 577-595. </span> <span style="word-break: break-all">https://doi.org/10.1007/s42064-024-0201-0</span> </div> <div class="v4-art-main-right-content"> </div> <el-collapse style="margin-top: 15px"> <el-collapse-item title="Metrics & Citations" name="4"> <template slot="title"> Metrics & Citations   <el-tooltip popper-class="v4-el-tooltip" effect="dark" content="Citation counts are pulled independently from Crossref, Web of Science, Scopus and CSCD. 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// 大纲和正文信息 var esmTextInfo = ''; var esmTextTitle = ''; // 正文所有的图片 var imgListInfo = []; // 所有的figer图片 var imgKeyListInfo = []; // 所有可以点击看大图的图片 var imgShowListInfo = []; //表格大纲信息 var tableListInfo = []; // 请求前缀 var contextPath = ''; var title = ''; var doi = "10.1007\/s42064-024-0201-0"; var showAI = 1; var articleKeyword = [{"id":"1840685757473853441","articleId":"1840680512333123585","keywordId":"1596017465603252226","keywordName":"circular restricted three-body problem (CR3BP)"},{"id":"1840685757612265475","articleId":"1840680512333123585","keywordId":"1840685757612265474","keywordName":"quasi-periodic torus"},{"id":"1840685757754871809","articleId":"1840680512333123585","keywordId":"1840685757750677505","keywordName":"heteroclinic connection"},{"id":"1840685757889089539","articleId":"1840680512333123585","keywordId":"1840685757889089538","keywordName":"knot theory"}]; var authors = {"authors":[{"id":"1840680514103119874","name":"<a href='\/scholar\/info?id=1840680514103119874'>Danny Owen<\/a>","email":"danny.owen@surrey.ac.uk","type":1,"companyId":null,"orcid":null,"firstAuthor":null,"sub":""},{"id":"1678232200955846658","name":"<a href='\/scholar\/info?id=1678232200955846658'>Nicola Baresi<\/a>","email":null,"type":2,"companyId":null,"orcid":null,"firstAuthor":null,"sub":""}],"companys":["<addr-line>Surrey Space Centre, University of Surrey, Guildford, UK<\/addr-line>"]}; var esmSize = 0; var articleId = "1840680512333123585"; var article = {"id":"1840680512333123585","title":"Applications of knot theory to the detection of heteroclinic connections between quasi-periodic orbits","doi":"10.1007\/s42064-024-0201-0","type":"2","journalId":"1424923732016201729","isOa":1,"clickNum":55,"downloadNum":12,"collectionNum":null,"cscdNum":0,"quoteNum":2,"articleNo":"astrodynamics-8-4-577","cover":null,"receivedTime":"2023-09-18T00:00:00.000+08:00","strReceivedTime":"18 September 2023","acceptedTime":"2024-01-16T00:00:00.000+08:00","strAcceptedTime":"16 January 2024","erratumId":null,"issueInfo":null,"issueInfoUrl":"<a href='\/journal\/join_journal\/archive?journalId=1424923732016201729\u0026volume=2024\u0026issn2522-008X'>2024, 8<\/a>(<a href='\/journal\/join_journal\/stage_page?stage=5\u0026id=1424923732016201729\u0026issueIndex=1840680635293339650\u0026issn2522-008X'>4<\/a>): 577-595","stageNum":5,"strType":"Research Article","strStage":"Issue","pubTime":"2024-04-15T17:13:13.000+08:00","pubYear":2024,"strPubTime":"15 April 2024","citationDate":"2024\/12\/01","erratum":null,"abstraction":"<p>Heteroclinic connections represent unique opportunities for spacecraft to transfer between isoenergetic libration point orbits for zero deterministic <inline-formula id=\"M1\"> <math id=\"mathml_M1\" display=\"inline\" overflow=\"scroll\"><mi mathvariant=\"normal\">\u0394<\/mi><mi>V<\/mi><\/math><\/inline-formula> expenditure. However, methods of detecting them can be limited, typically relying on human-in-the-loop or computationally intensive processes. In this paper we present a rapid and fully systematic method of detecting heteroclinic connections between quasi-periodic invariant tori by exploiting topological invariants found in knot theory. The approach is applied to the Earth\u2013Moon, Sun\u2013Earth, and Jupiter\u2013Ganymede circular restricted three-body problems to demonstrate the robustness of this method in detecting heteroclinic connections between various quasi-periodic orbit families in restricted astrodynamical problems.<\/p>","abstractImage":"<img src=\"https:\/\/wqketang.oss-cn-beijing.aliyuncs.com\/zip-unzip\/zip-7679846b-b79a-4580-b2f0-b60ef155f0cf\/astrodynamics-8-4-577\/files\/astrodynamics-8-4-577-FE1.jpg?Expires=1732391120\u0026amp;OSSAccessKeyId=STS.NSpqk4tC6Ru5rkHhuNvgjaw2W\u0026amp;Signature=fmdxzi9zujWeciz7IHDqkvRzAdY%3D\u0026amp;security-token=CAISywJ1q6Ft5B2yfSjIr5DFOtGAmZwX5bfecE35jHUbeuhGjrKZtTz2IHtKenhsBOsbtfk1mG5W5%2FgZlqJ9SptIAEfJa9d99MyFR9AuvtCT1fau5Jko1beHewHKeTOZsebWZ%2BLmNqC%2FHt6md1HDkAJq3LL%2Bbk%2FMdle5MJqP%2B%2FUFB5ZtKWveVzddA8pMLQZPsdITMWCrVcygKRn3mGHdfiEK00he8TouufTinpHMskGA1Aell7Mvyt6vcsT%2BXa5FJ4xiVtq55utye5fa3TRYgxowr%2Fwo0v0YpGya5YzHXwcPskvdKZbo78UqLQlla6w%2BGqFJqvPxr%2Fp8t%2Fx5fWJKAezhVgs8cVM8JOjIqKOscIsihmul4wzFcD1LXoQ6vH1ZZ5%2FAzVZaVWUEMpNqcRxTMldXaQqhSZT8m3upKXzOJeX7ls9%2Fv%2FV7p%2BNtHbjUTzDnGoABljLYqvsZH%2Fp3c6u5%2Fh4ZYrxRVq3ZNuFgFMmVvR2CogbYHFpJghu8z%2F7O5gd8c4FZsBbKYjwXQrg4p2p3vLN%2F3yaKBOhOAzsG6irYr%2BhBCVqQnaSsB79uIP4fdoDCX3VF5C5XeKQFVt9mQsRRryO0UVkpaC%2BJZfNNkFWId5FB6p0gAA%3D%3D\">","abstractToc":null,"acknowledgement":null,"copyright":"\u00A9 The Author(s) 2024","pdfSize":"(6.5 MB)","isCollection":false,"journalIssn":"2522-008X","issueId":"1840680635293339650","revised":null,"issueDate":" December 2024","serviceAddress":null,"price":0.0,"subject":null,"subjects":null,"license":"<p>This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.<\/p>\n<p>The images or other third party material in this article are included in the article\u2019s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article\u2019s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.<\/p>\n<p>To view a copy of this license, visit <a ext-link-type=\"uri\" href=\"http:\/\/creativecommons.org\/licenses\/by\/4.0\/\">http:\/\/creativecommons.org\/licenses\/by\/4.0\/<\/a>.<\/p>","ifErratum":false,"webOfScienceNum":1,"scopusNum":1,"trendMd":"81479","trendMdHtml":"<div id=\"trendmd-suggestions\"><\/div>\n <script defer src='\/\/js.trendmd.com\/trendmd.min.js' data-trendmdconfig='{\"journal_id\":\"81479\", \"element\":\"#trendmd-suggestions\"}'><\/script>","articleRecommendVos":null,"issue":"4","volume":"8","page":"Pages 577-595","citationPublicationDate":"2024\/4\/15","issueTime":"2024\/12\/1","authorAndCompanyVOS":[{"author":"Danny Owen","company":"Surrey Space Centre,University of Surrey, GU2 7XH,"},{"author":"Nicola Baresi","company":"Surrey Space Centre,University of Surrey, GU2 7XH,"}],"citationAuthorInstitution":null,"journalOrgan":"\u6E05\u534E\u5927\u5B66\u51FA\u7248\u793E","altmetricTwo":null,"keypointsAbstracted":null,"isMerge":null,"articleCiteVO":{"author":"Owen D, Baresi N. 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Homoclinic and heteroclinic solutions in the restricted three-body problem. <i>Celestial Mechanics<\/i>, <strong>1988<\/strong>, 44(3): 239\u2013259.<\/p>","keyStr":"b6","label":"[6]","content":null,"num":null,"doi":"10.1007\/BF01235538","link":"https:\/\/scholar.google.com\/scholar_lookup?title=Homoclinic and heteroclinic solutions in the restricted three-body problem\u0026journal=Celestial Mechanics\u0026volume=44\u0026pages=239-259\u0026publication_year=1988\u0026author=G\u00F3mez G.\u0026author=Llibre J.\u0026author=Masdemont J."},{"id":"1840685758031695874","articleId":null,"reference":"<p>G\u00F3mez, G., Masdemont, J. Some zero cost transfers between libration point orbits. <i>Advances in the Astronautical Sciences<\/i>, <strong>2000<\/strong>, 105(2): 1199\u20131216.<\/p>","keyStr":"b7","label":"[7]","content":null,"num":null,"doi":"","link":"https:\/\/scholar.google.com\/scholar_lookup?title=Some zero cost transfers between libration point orbits\u0026journal=Advances in the Astronautical Sciences\u0026volume=105\u0026pages=1199-1216\u0026publication_year=2000\u0026author=G\u00F3mez G.\u0026author=Masdemont J."},{"id":"1840685758035890178","articleId":null,"reference":"Arona, L., Masdemont, J. J. Computation of heteroclinic orbits between normally hyperbolic invariant 3-spheres foliated by 2-dimensional invariant Tori in Hill\u2019s problem. In: <i>Conference Publications<\/i>. 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generators were installed on sloping buildings such as houses to achieve large-scale raindrop energy harvesting easily. 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generators were installed on sloping buildings such as houses to achieve large-scale raindrop energy harvesting easily. Reprinted with permission from <i>iEnergy</i>, 2(2): 93–99, 2023 © 2023 The Author(s)</p>\n</fig>", // "contentHtml": "<img id=\"image-iEng-2023-s-0024-1\" onclick=\"showImage(event,this)\" src=\"https://wqketang.oss-cn-beijing.aliyuncs.com/zip-unzip/zip-7f9b22ae-5865-4143-a681-f77a8724f8dd/iEng-2023-s-0024/files/iEng-2023-s-0024-1.jpg?Expires=1719580654&OSSAccessKeyId=STS.NUbZf2DD6Ue3FqTmGvgkvUbF1&Signature=%2BhRmDGIUtD9EkRxdDzgF%2FWU9dDE%3D&x-oss-process=image%2Fresize%2Cm_fixed%2Cw_600&security-token=CAISywJ1q6Ft5B2yfSjIr5bXEdyGqZsX4qfYRFfliUcja%2BRauqft0zz2IHtKenhsBOsbtfk1mG5W5%2FgZlqJ9SptIAEfJa9d99Mz%2Bf8BIjdCT1fau5Jko1beHewHKeTOZsebWZ%2BLmNqC%2FHt6md1HDkAJq3LL%2Bbk%2FMdle5MJqP%2B%2FUFB5ZtKWveVzddA8pMLQZPsdITMWCrVcygKRn3mGHdfiEK00he8TouufTinpHMskGA1Aell7Mvyt6vcsT%2BXa5FJ4xiVtq55utye5fa3TRYgxowr%2Fwo0v0YpGya5YzHXwcPskvdKZbo78UqLQlla6w%2BGqFJqvPxr%2Fp8t%2Fx5fWJKAezhVgs8cVM8JOjIqKOscIsiZmYk4pM4wgzSyCaJL7f%2FhREKa7znWGyxgyLY25K9yOXNh%2FA7x25WFZknm%2BbJoNLmr0pOOvEupyi0697UTzDnGoABihsmGXKWpSd6XDZIstjWbPKKorqYDJSMThEt%2F%2F9EPJXR4F4eCQ9BJV3gUyzfY08MnHKQ4H7mG8WnZ8%2FjZiwrfF7NSWXWD8SUf46hbaSsKbigUEcuiHoLO8%2BpSp%2BiEOlDNxxej3LE4vOpbeaqnNSNZFXt3nMTNC1HaeHqNJS7lYcgAA%3D%3D\">", // "name": "graphic" // } // ], // "imgKeyList": [ // "image-iEng-2023-s-0024-1" // ], // "tabKeyList": [], // "tables": [], // "fullTextUrl": "https://wqketang.oss-cn-beijing.aliyuncs.com/other/journal_prod/2024-06-28/3098b740-7b52-44b7-88a9-92fedc8988db.gif?Expires=1719560854&OSSAccessKeyId=STS.NUbZf2DD6Ue3FqTmGvgkvUbF1&Signature=1K7ZtLBP2mEeczlPMrOHw4aoGus%3D&security-token=CAISywJ1q6Ft5B2yfSjIr5bXEdyGqZsX4qfYRFfliUcja%2BRauqft0zz2IHtKenhsBOsbtfk1mG5W5%2FgZlqJ9SptIAEfJa9d99Mz%2Bf8BIjdCT1fau5Jko1beHewHKeTOZsebWZ%2BLmNqC%2FHt6md1HDkAJq3LL%2Bbk%2FMdle5MJqP%2B%2FUFB5ZtKWveVzddA8pMLQZPsdITMWCrVcygKRn3mGHdfiEK00he8TouufTinpHMskGA1Aell7Mvyt6vcsT%2BXa5FJ4xiVtq55utye5fa3TRYgxowr%2Fwo0v0YpGya5YzHXwcPskvdKZbo78UqLQlla6w%2BGqFJqvPxr%2Fp8t%2Fx5fWJKAezhVgs8cVM8JOjIqKOscIsiZmYk4pM4wgzSyCaJL7f%2FhREKa7znWGyxgyLY25K9yOXNh%2FA7x25WFZknm%2BbJoNLmr0pOOvEupyi0697UTzDnGoABihsmGXKWpSd6XDZIstjWbPKKorqYDJSMThEt%2F%2F9EPJXR4F4eCQ9BJV3gUyzfY08MnHKQ4H7mG8WnZ8%2FjZiwrfF7NSWXWD8SUf46hbaSsKbigUEcuiHoLO8%2BpSp%2BiEOlDNxxej3LE4vOpbeaqnNSNZFXt3nMTNC1HaeHqNJS7lYcgAA%3D%3D", // "glossary": [], // "notes": [], // "fundingStatements": [], // "app": [], // "fn": [], // "bio": [] // }; if (fullTextInfo['glossary']['length'] > 0) { for (var gl = 0; gl < fullTextInfo['glossary']['length']; gl++) { treeDataO.push({ id: 'content_title_-4_' + gl, label: fullTextInfo['glossary'][gl]['title'] }); } } // 正文 if (fullTextInfo['trees'].length > 0) { fullTextInfo['trees'].forEach(item => { if (item.key !== 'esm1') { var nodeC = { id: 'content_' + item.key, label: item.title, children: [] }; if (item.children && item.children.length > 0) { allOutlineShow = true; item.children.forEach(child => { if (child.key !== 'esm1') { var nodeS = { id: 'content_' + child.key, label: child.title, children: [] }; if (child.children && child.children.length > 0) { child.children.forEach(son => { if (son.key !== 'esm1') { nodeS.children.push({ id: 'content_' + son.key, label: son.title, children: [] }); } }); } nodeC.children.push(nodeS); } }); } treeDataO.push(nodeC); } }); } // app 附录 if (fullTextInfo['app']['length'] > 0) { for (var ap = 0; ap < fullTextInfo['app']['length']; ap++) { treeDataO.push({ id: 'content_title_-5_' + ap, label: fullTextInfo['app'][ap]['title'] }); } } // fn 脚注 if (fullTextInfo['fn']['length'] > 0) { treeDataO.push({ id: 'content_title_-6', label: 'Annotation' }); } // esm if (article.strType !== 'Issue Information') { treeDataO.push({ id: 'content_title_-11', label: 'Electronic Supplementary Material' }); } // ack 致谢 if (article['acknowledgement']) { treeDataO.push({ id: 'content_title_-7', label: 'Acknowledgements' }); } // funding-statement 基金 if (fullTextInfo['fundingStatements']['length'] > 0) { treeDataO.push({ id: 'content_title_-8', label: 'Funding' }); } // notes [ 伦理声明,知情同意书, 利益声明,作者声明,数据声明] if (fullTextInfo['notes']['length'] > 0) { for (var no = 0; no < fullTextInfo['notes'].length; no++) { treeDataO.push({ id: 'content_title_-10_' + no, label: fullTextInfo['notes'][no]['title'] }); } } // 参考文献 if (referenceList && referenceList['length'] > 0) { treeDataO.push({ id: 'content_title_-12', label: 'References' }); } // bio 作者简介 if (fullTextInfo['bio']['length'] > 0) { treeDataO.push({ id: 'content_title_-13', label: 'Author biography' }); } // 大纲hover时显示title var reg = /<\/?.+?\/?>/g; treeDataO.forEach(item => { item.labelWord = item['label'].replace(reg, ''); if (item.children && item.children.length > 0) { item.children.forEach(child => { child.labelWord = child.label.replace(reg, ''); if (child.children && child.children.length > 0) { child.children.forEach(son => { son.labelWord = son.label.replace(reg, ''); }); } }); } }); articleApp.treeData = treeDataO; articleApp.imgMenuList = fullTextInfo['figImages']; articleApp.tableMenuList = fullTextInfo['tabKeyList']; //所有fig图片/大纲信息 imgKeyListInfo = fullTextInfo['imgKeyList']; // 正文所有的图片 imgListInfo = fullTextInfo['images']; // 可以点击看大图的图片 imgShowListInfo = []; if (imgListInfo.length > 0) { imgListInfo.forEach(item => { if (item['parentHtml'].indexOf('class="inline-graphic"') < 0) { imgShowListInfo.push(item); } }); // 缩略图大图查看 var imageBigHtml = ''; if (imgShowListInfo.length > 0) { for (var m = 0; m < imgShowListInfo.length; m++) { imageBigHtml = imageBigHtml + '<li>' + '<div>' + imgShowListInfo[m]['parentHtml'] + '</div>' + '</li>'; } } $('#content_img').html(imageBigHtml); } //表格大纲信息 tableListInfo = fullTextInfo['tables']; if (tableListInfo.length > 0) { // 表格查看大图 var tableBig1Html = ''; var tableBig2Html = ''; if (tableListInfo.length > 0) { for (var n = 0; n < tableListInfo.length; n++) { tableBig1Html = '<div class="swiper-slide" style="background-color: #fff">' + '<div class="ahc-content" style="max-height: 100%; width: 100%; padding: 20px; overflow: auto">' + tableListInfo[n]['parentHtml'] + '</div>' + '</div>'; tableBig2Html = '<div class="swiper-slide table-big-view" style="cursor: pointer">' + tableListInfo[n]['html'] + '</div>'; $('#insert_table_big_1').append(tableBig1Html); $('#insert_table_big_2').append(tableBig2Html); } } } // 正文信息 $.ajax({ url: fullTextInfo['fullTextUrl'], // url: 'http://localhost:8733/assets/fig-test.gif', type: 'get', success: function(data) { fullTextInfo['contentList'] = JSON.parse(data); // glossary if (fullTextInfo['glossary']['length'] > 0) { $('#title_-4').css('display', 'block'); var dom = ''; for (var g = 0; g < fullTextInfo['glossary']['length']; g++) { dom = dom + '<div class="v4-art-content-p">' + '<div class="glossary-item" id="title_-4_' + g + '">' + '<h2>' + fullTextInfo['glossary'][g]['title'] + '</h2>' + '<div>' + fullTextInfo['glossary'][g]['content'] + '</div>' + '</div>' + '</div>'; } dom = dom + '<div style="clear: both;"></div>'; $('#title_-4').html(dom); } // 正文 var contentHtml = ''; var contentHtml2 = ''; esmTextInfo = ''; esmTextTitle = ''; if (fullTextInfo['contentList'] && fullTextInfo['contentList']['length'] > 0) { for (var s = 0; s < fullTextInfo['contentList'].length; s++) { // 处理图片 for (var i = 0; i < imgListInfo['length']; i++) { const mergImg = new RegExp(`<img[^>]*id="${imgListInfo[i]['key']}"[^>]*>`, 'i'); if (imgListInfo[i]['contentHtml'].indexOf('class="inline-graphic"') < 0) { // 是否是fig图片 var ifFig = false; for (var ii = 0; ii < imgKeyListInfo.length; ii++) { if (imgListInfo[i]['contentHtml'].indexOf(imgKeyListInfo[ii]) > 0) { ifFig = true; } } if (ifFig) { fullTextInfo['contentList'][s]['content'] = fullTextInfo['contentList'][s]['content'].replace(mergImg, imgListInfo[i]['contentHtml'] + '<div class="v4-art-image">\n' + ' <span onclick="showImageBtn(event, \'' + imgListInfo[i]['key'] + '\')">View original image</span>\n' + ' <span onclick="downloadImageBtn(event, \'' + imgListInfo[i]['key'] + '\')">Download original image</span>\n' + ' </div>'); } else { fullTextInfo['contentList'][s]['content'] = fullTextInfo['contentList'][s]['content'].replace(mergImg, imgListInfo[i]['contentHtml']); } } else { fullTextInfo['contentList'][s]['content'] = fullTextInfo['contentList'][s]['content'].replace(mergImg, imgListInfo[i]['contentHtml']); } } // 处理正文的脚注内容，实现定位 const xrefFn = new RegExp(`ref-type="fn"`, 'gi'); fullTextInfo['contentList'][s]['content'] = fullTextInfo['contentList'][s]['content'].replace(xrefFn, 'ref-type="fn" onclick="findFnById(event)"'); // 正文内出现esm说明文字内容 if (fullTextInfo['contentList'][s]['key'] === 'esm1') { esmTextInfo = fullTextInfo['contentList'][s]['content']; esmTextTitle = fullTextInfo['contentList'][s]['title']; } else { contentHtml = contentHtml + '<div class="v4-art-content-p" id="' + fullTextInfo['contentList'][s]['key'] + '">' + '<h2 >' + fullTextInfo['contentList'][s]['title'] + '</h2>' + '<div style="overflow-x: auto; overflow-y: hidden;">' + fullTextInfo['contentList'][s]['content'] + '</div>' + '</div>'; } } } // app if (fullTextInfo['app']['length'] > 0) { for (var a = 0; a < fullTextInfo['app']['length']; a++) { contentHtml = contentHtml + '<div class="v4-art-content-p" id="title_-5_' + a + '">' + '<h2>' + fullTextInfo['app'][a]['label'] + fullTextInfo['app'][a]['title'] + '</h2>' + '<div style="overflow-x: auto; overflow-y: hidden;">' + fullTextInfo['app'][a]['content'] + '</div>' + '</div>'; } } // fn if (fullTextInfo['fn']['length'] > 0) { contentHtml = contentHtml + '<div class="v4-art-content-p" id="title_-6">' + '<h2 class="content-title">' + 'Annotation' + '</h2>'; for (var f = 0; f < fullTextInfo['fn']['length']; f++) { contentHtml = contentHtml + '<div class="fn-item">' + '<span style="cursor: pointer;" id="f_' + fullTextInfo['fn'][f]['key'] + '" onclick="findFnInContentById(this)">' + fullTextInfo['fn'][f]['title'] + '</span>' + '<div>' + fullTextInfo['fn'][f]['content'] + '</div>' + '</div>'; } contentHtml = contentHtml + '</div>'; } // 正文内的esmText放到esm位置 if (esmTextInfo) { if (esmSize > 0) { $('#esm_text').html(esmTextInfo); $('#esm_text').css('display', 'block'); $('#esm_title').html(esmTextTitle); } else if (esmSize < 0) { contentHtml = contentHtml + '<div class="v4-art-content-p" id="title_-11">' + '<h2 class="content-title">' + esmTextTitle + '</h2>' + '<div style="overflow-x: auto; overflow-y: hidden;">' + esmTextInfo + '</div>' + '</div>'; } treeDataO.forEach((item) => { if (item.id === 'content_title_-11') { item.label = esmTextTitle; item.labelWord = esmTextTitle; articleApp.treeData = treeDataO; } }); } else { if (esmSize === 0) { treeDataO.forEach((item, index) => { if (item.id === 'content_title_-11') { treeDataO.splice(index, 1); articleApp.treeData = treeDataO; } }); } } articleApp.treeDataReady = true; // ack if (article['acknowledgement']) { contentHtml2 = contentHtml2 + '<div class="v4-art-content-p" id="title_-7">' + '<h2 class="content-title">' + 'Acknowledgements' + '</h2>' + '<div style="overflow-x: auto; overflow-y: hidden;">' + article['acknowledgement'] + '</div>' + '</div>'; } // funding-statement if (fullTextInfo['fundingStatements']['length'] > 0) { contentHtml2 = contentHtml2 + '<div class="v4-art-content-p" id="title_-8">' + '<h2 class="content-title">' + 'Funding' + '</h2>'; for (var fs = 0; fs < fullTextInfo['fundingStatements']['length']; fs++) { contentHtml2 = contentHtml2 + '<div class="fs-item"><p>' + fullTextInfo['fundingStatements'][fs] + '</p></div>'; } contentHtml2 = contentHtml2 + '</div>'; } // notes if (fullTextInfo['notes']['length'] > 0) { contentHtml2 = contentHtml2 + '<div class="v4-art-content-p" id="title_-10">'; for (var n = 0; n < fullTextInfo['notes']['length']; n++) { contentHtml2 = contentHtml2 + '<div class="notes-item" id="title_-10_' + n + '">' + '<h2>' + fullTextInfo['notes'][n]['title'] + '</h2>' + '<div>' + fullTextInfo['notes'][n]['content'] + '</div>' + '</div>'; } contentHtml2 = contentHtml2 + '</div>'; } // bio var contentHtmlBio = ''; if (fullTextInfo['bio']['length'] > 0) { contentHtmlBio = contentHtmlBio + '<div class="v4-art-content-p" id="title_-13" style="min-height: 200px;">' + '<h2>' + 'Author biography' + '</h2>'; for (var b = 0; b < fullTextInfo['bio']['length']; b++) { contentHtmlBio = contentHtmlBio + '<div class="bio-item">' + (fullTextInfo['bio'][b]['path'] ? '<img src="' + fullTextInfo['bio'][b]['path'] + '">' : '') + '<div>' + fullTextInfo['bio'][b]['content'] + '</div>' + '</div>'; } contentHtmlBio = contentHtmlBio + '<div style="clear: both"></div></div>'; } $('#insert_content_one').prepend(contentHtml); $('#insert_content_two').prepend(contentHtml2); $('#insert_content').append(contentHtmlBio); setTimeout(function() { if ($('#insert_content .v4-art-content-p').last().height() < 500) { $('#insert_content .v4-art-content-p').last().css('padding-bottom', '500px'); } }, 1000); MathJax.Hub.Queue(['Typeset', MathJax.Hub]); // 渲染好数据之后，； setTimeout(function() { // 图片大图模态初始化 if (document.getElementById('content_img')) { preViewImage = new Viewer(document.getElementById('content_img'), { url: 'original-src', }); } // 表格大图查看初始化 initSwiper(); initTagClickHandler(); // 插入查看表格按钮如果是移动端去掉表格模态查看 => 屏幕小于600 去掉表格查看 if ($(window).width() > 600) { var tableDom = $('#insert_content table'); for (var ta = 0; ta < tableDom.length; ta++) { if ($($('#insert_content table')[ta]).attr('id')) { // 判断 if (tableListInfo.length > 0) { let haveT = false; for (let tt = 0; tt < tableListInfo.length; tt++) { if ($($('#insert_content table')[ta]).attr('id') == tableListInfo[tt]['key']) { haveT = true; } } if (haveT) { var b = document.createElement('div'); b.setAttribute('onclick', 'showTableBtn(this)'); b.setAttribute('class', 'v4-art-table'); b.innerText = 'Show table'; $($('#insert_content table')[ta]).parent().parent().append(b); } } } } } // 左侧大纲节点 domArr = $('.v4-art-content-p'); // 是否显示show outline setTimeout(() => { if (allOutlineShow) { $(".v4_art_outline_show").css('display', 'block'); } }, 300); }, 10); if ( fullTextInfo['glossary']['length'] === 0 && (!fullTextInfo['contentList'] || fullTextInfo['contentList']['length'] === 0) && fullTextInfo['app']['length'] === 0 && fullTextInfo['fn']['length'] === 0 && (!esmTextInfo && esmSize === 0) && !article['acknowledgement'] && fullTextInfo['fundingStatements']['length'] === 0 && fullTextInfo['notes']['length'] === 0 && fullTextInfo['bio']['length'] === 0 && referenceList['length'] === 0 && !article.clcNumber && !article.documentsCode && !article.articleCodeId && !article.abstraction && !article.abstractToc && !article.abstractImage && !article['keypointsAbstracted'] && !article.erratum && articleKeyword.length === 0 ) { $('#article_no_data').css('display', 'block'); } }, error: function(err) { alert(err.toString()); }, }); }, error: function(err) { alert(err.toString()); }, }); } // 进入页面时执行 // 组装大纲 // key-points Highlights keypointsAbstracted if (article['keypointsAbstracted'] != null) { treeDataO.push({ id: 'content_title_-1', label: article['keypointsAbstracted']['title'] }); } // 摘要 article.abstractImage != null if ((article.abstractImage != null && article.abstractImage != '') || (article.abstractToc != null && article.abstractToc != '')) { treeDataO.push({ id: 'content_title_-2-1', label: 'Graphical Abstract' }); } // 摘要 article.abstraction != null || (article.abstractToc != null && article.abstractToc != '') if (article.abstraction != null && article.abstraction != '') { treeDataO.push({ id: 'content_title_-2', label: 'Abstract' }); } // 关键词 if (articleKeyword.length>0) { treeDataO.push({ id: 'content_title_-3', label: 'Keywords' }); } // CLC number 2024-7-8 大纲中去掉CLC Number显示 // if ((article.clcNumber != null && article.clcNumber != '') || (article.documentsCode != null && article.documentsCode != '') // || (article.articleCodeId != null && article.articleCodeId != '')) { // treeDataO.push({ id: 'content_title_clc', label: 'CLC number' }); // } // 处理摘要图片 if (article.abstractImage) { var abstractImgStrBig = '<img ' + 'original-src=' + $('#v4_art_abstract_img img').attr('src'); $('#content_img_abstract').html('<li>' + article.abstractImage.replace('<img', abstractImgStrBig) + '</li>'); var abstractImgStr = '<img id="v4-art-abstract-img" onclick="showImageBtn(event, \'v4-art-abstract-img\')" ' + 'original-src=' + $('#v4_art_abstract_img img').attr('src'); $('#v4_art_abstract_img').html(article.abstractImage.replace('<img', abstractImgStr)); var dom = '<div class="v4-art-image">\n' + ' <span onclick="showImageBtn(event, \'v4-art-abstract-img\')">View original image</span>\n' + ' <span onclick="downloadImageBtn(event, \'v4-art-abstract-img\')">Download original image</span>\n' + ' </div>'; $('#v4_art_abstract_img').parent().append(dom); setTimeout(() => { // 图片大图模态初始化 if (document.getElementById('content_img_abstract')) { preViewImage = new Viewer(document.getElementById('content_img_abstract'), { url: 'original-src', }); } }, 10); } // 如果显示正文内容加载正文，不显示正文时，拼接显示增强出版资源、参考文献 if (ifShowFullText && article.strType !== 'Issue Information') { // 加载文章内容 loadFullTextInfo(); } else { // esm if (esmSize > 0) { treeDataO.push({ id: 'content_title_-11', label: 'Electronic Supplementary Material', labelWord: 'Electronic Supplementary Material', }); } // 参考文献 if (referenceList && referenceList['length'] > 0) { treeDataO.push({ id: 'content_title_-12', label: 'References' }); } articleApp.treeData = treeDataO; articleApp.treeDataReady = true; if ( esmSize === 0 && referenceList['length'] === 0 && !article.clcNumber && !article.documentsCode && !article.articleCodeId && !article.abstraction && !article.abstractToc && !article.abstractImage && !article['keypointsAbstracted'] && !article.erratum && articleKeyword === 0 ) { $('#article_no_data').css('display', 'block'); } } // 初始化图片表格轮播 function initSwiper() { // 初始化正文表格模态显示 galleryTopTable = new Swiper('.gallery-top-table', { nextButton: '.swiper-button-next-table', prevButton: '.swiper-button-prev-table', spaceBetween: 10, }); galleryThumbsTable = new Swiper('.gallery-thumbs-table', { spaceBetween: 10, centeredSlides: true, slidesPerView: 'auto', touchRatio: 0.2, slideToClickedSlide: true, }); galleryTopTable.params.control = galleryThumbsTable; galleryThumbsTable.params.control = galleryTopTable; } // 加载Altmetrics 是否存在 function isAltmetrics() { $.ajax({ // url: contextPath + '/article/altmetric?doi=' + doi, url: 'https://api.altmetric.com/v1/doi/' + doi, type: 'get', dataType: 'json', contentType: 'application/json', success: function(data) { if (data.score > 0) { $('#article_altmetric').css('display', 'block'); } }, error: function(err) { // alert(err.toString()); console.log(err); }, }); } setTimeout(function() { isAltmetrics(); }, 1000); // 点击图片显示大图 function showImage(event, dom) { if ($(dom).attr('class') !== 'inline-graphic') { event.stopPropagation(); var id = $(dom).attr('id'); var index = 0; for (var i = 0; i < imgShowListInfo.length; i++) { if (imgShowListInfo[i]['key'] === id) { index = i; $($('#content_img').children()[index]).find('img').click(); } } } } function showImageBtn(event, id) { event.stopPropagation(); if (id === 'v4-art-abstract-img') { $($('#content_img_abstract').children()[0]).find('img').click(); } else { var index = 0; for (var i = 0; i < imgShowListInfo.length; i++) { if (imgShowListInfo[i]['key'] === id) { index = i; $($('#content_img').children()[index]).find('img').click(); } } } } // 下载原图 function downloadImageBtn(event, id) { event.stopPropagation(); $.ajax({ url: contextPath + '/article/img/download?path=' + $('#' + id).attr('src'), type: 'get', dataType: 'json', contentType: 'application/json', success: function(data) { if ($(window).width() < 800) { window.location.href = data.object; } else { window.open(data.object); } }, error: function(err) { alert(err.toString()); }, }); } // 点击表格模态显示表格 function showTable(event) { return; // 如果是移动端去掉表格模态查看 => 屏幕小于600 去掉表格查看 if ($(window).width() < 600) { return; } var id = $(event).attr('id'); var index = 0; for (var i = 0; i < tableListInfo.length; i++) { if (tableListInfo[i]['key'] === id) { index = i; galleryTopTable.slideTo(index, 100, false); galleryThumbsTable.slideTo(index, 100, false); setTimeout(function() { $('.article-html-table-modal').css('margin-left', 0); }, 200); } } } function showTableBtn(event) { var id = $($(event).prev().children()[0]).attr('id'); var index = 0; for (var i = 0; i < tableListInfo.length; i++) { if (tableListInfo[i]['key'] === id) { index = i; galleryTopTable.slideTo(index, 100, false); galleryThumbsTable.slideTo(index, 100, false); setTimeout(function() { $('.article-html-table-modal').css('margin-left', 0); }, 200); } } } // 关闭模态 function closeModal() { $('.article-html-table-modal').css('margin-left', '-100%'); } // 新增轮询检测用户停留时间 $(document).ready(function() { setInterval(function() { $.ajax({ url: '/article/statistical_duration?id=' + articleId + '&uuid=' + uuid, type: 'get', }); }, 5000); }); // 统计下载量 function countDownLoadNum(id, ifPreview) { $.ajax({ url: contextPath + '/article/stat?articleId=' + id + '&ifPreview=' + ifPreview, type: 'get', dataType: 'json', contentType: 'application/json', }); } var user = null; function send_email(authorId, articleId) { if (user != null) { location.href = contextPath + '/user/user/article/send_email?authorId=' + authorId + '&articleId=' + articleId; } else { showYxAlert('warning', 'You are not currently logged in, please log in and operate!'); var code = window.location.pathname; var param = window.location.search; location.href = '/user/user/login_forward?tag=5&code=' + encodeURIComponent(code + param); } } // 点击xref标签跳转 function initTagClickHandler() { $('xref').click(function(event) { event = event || window.event; event.stopPropagation ? event.stopPropagation() : (event.cancelBubble = true); var refType = $(this).attr('ref-type'); var id = $(this).attr('rid'); switch (refType) { // 表格 case 'table': { var dom = $('#' + id).parent(); break; } // 图片 case 'fig': // 章节 case 'sec': // 公式 case 'disp-formula': { var dom = $('#' + id); break; } default: { } } jumpToId(dom); }); $('.html-table-content label').click(function() { var tableDom = $(this).closest('.html-table-content'); jumpToId(tableDom); }); $('fig label').click(function() { var figDom = $(this).closest('fig'); jumpToId(figDom); }); } function jumpToId(dom) { if (!dom) { return; } $(window).scrollTop(dom.offset().top - 100); dom.css('backgroundColor', '#eee'); setTimeout(function() { dom.css('backgroundColor', 'initial'); }, 1000); } // 正文节点滚动到可视范围内，选中展开对应的节点 $(window).scroll(function() { // 正文节点滚动到可视范围内，选中展开对应的节点 for (var d = 0; d < domArr.length; d++) { const domRect = domArr[d].getBoundingClientRect(); if (domRect.top < 150 && domRect.top > 0) { articleApp.setSelectedKey('content_' + $(domArr[d]).attr('id')); return; } if (domRect.bottom > 500 && domRect.top < 0) { articleApp.setSelectedKey('content_' + $(domArr[d]).attr('id')); return; } } }); window.addEventListener('scroll', function() { // 不显示正文的时候不统计浏览量 if (!ifShowFullText) { return } // 滚动到正文部分的时候掉接口 if (time > 1000 * 60 * 5 || num === 0) { if (document.getElementById('insert_content').getBoundingClientRect().top <= 150) { time = 0; num = num + 1; countDownLoadNum(articleId, ifPreview); } } }); var time = 0; var num = 0; var interval = setInterval(function() { time = time + 1000; }, 1000); window.addEventListener('beforeunload', (event) => { // 在这里执行你的清理工作 clearInterval(interval); }); </script> </html>

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Applications of knot theory to the detection of heteroclinic connections between quasi-periodic orbits