Variational order for forced Lagrangian systems II. Euler-Poincaré equations with forcing
In this paper we provide a variational derivation of the Euler-Poincaré equations for systems subjected to external forces using an adaptation of the techniques introduced by Galley and others Martín de Diego and Martín de Almagro (2018 Nonlinearity 31 3814-3846), Galley (2013 Phys. Rev. Lett. 110 1...
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Veröffentlicht in: | Nonlinearity 2020-08, Vol.33 (8), p.3709-3738 |
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description | In this paper we provide a variational derivation of the Euler-Poincaré equations for systems subjected to external forces using an adaptation of the techniques introduced by Galley and others Martín de Diego and Martín de Almagro (2018 Nonlinearity 31 3814-3846), Galley (2013 Phys. Rev. Lett. 110 174301), Galley et al (2014 (arXiv:[math-Ph] 1412.3082)). Moreover, we study in detail the underlying geometry which is related to the notion of Poisson groupoid. Finally, we apply the previous construction to the formal derivation of the variational error for numerical integrators of forced Euler-Poincaré equations and the application of this theory to the derivation of geometric integrators for forced systems. |
doi_str_mv | 10.1088/1361-6544/ab8bb1 |
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Euler-Poincaré equations with forcing</title><source>IOP Publishing Journals</source><source>Institute of Physics (IOP) Journals - HEAL-Link</source><creator>Martín de Diego, D ; Martín de Almagro, R T Sato</creator><creatorcontrib>Martín de Diego, D ; Martín de Almagro, R T Sato</creatorcontrib><description>In this paper we provide a variational derivation of the Euler-Poincaré equations for systems subjected to external forces using an adaptation of the techniques introduced by Galley and others Martín de Diego and Martín de Almagro (2018 Nonlinearity 31 3814-3846), Galley (2013 Phys. Rev. Lett. 110 174301), Galley et al (2014 (arXiv:[math-Ph] 1412.3082)). Moreover, we study in detail the underlying geometry which is related to the notion of Poisson groupoid. Finally, we apply the previous construction to the formal derivation of the variational error for numerical integrators of forced Euler-Poincaré equations and the application of this theory to the derivation of geometric integrators for forced systems.</description><identifier>ISSN: 0951-7715</identifier><identifier>EISSN: 1361-6544</identifier><identifier>DOI: 10.1088/1361-6544/ab8bb1</identifier><identifier>CODEN: NONLE5</identifier><language>eng</language><publisher>IOP Publishing</publisher><subject>Euler-Poincaré equations ; forced systems ; geometric integration ; variational integrators</subject><ispartof>Nonlinearity, 2020-08, Vol.33 (8), p.3709-3738</ispartof><rights>2020 IOP Publishing Ltd & London Mathematical Society</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c310t-147ed29aea2df84f26609e78eb0408d10020cbc084db4a31ec8ea1ba24df8d113</citedby><cites>FETCH-LOGICAL-c310t-147ed29aea2df84f26609e78eb0408d10020cbc084db4a31ec8ea1ba24df8d113</cites><orcidid>0000-0001-6762-8909</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://iopscience.iop.org/article/10.1088/1361-6544/ab8bb1/pdf$$EPDF$$P50$$Giop$$H</linktopdf><link.rule.ids>314,776,780,27901,27902,53821,53868</link.rule.ids></links><search><creatorcontrib>Martín de Diego, D</creatorcontrib><creatorcontrib>Martín de Almagro, R T Sato</creatorcontrib><title>Variational order for forced Lagrangian systems II. Euler-Poincaré equations with forcing</title><title>Nonlinearity</title><addtitle>Non</addtitle><addtitle>Nonlinearity</addtitle><description>In this paper we provide a variational derivation of the Euler-Poincaré equations for systems subjected to external forces using an adaptation of the techniques introduced by Galley and others Martín de Diego and Martín de Almagro (2018 Nonlinearity 31 3814-3846), Galley (2013 Phys. Rev. Lett. 110 174301), Galley et al (2014 (arXiv:[math-Ph] 1412.3082)). Moreover, we study in detail the underlying geometry which is related to the notion of Poisson groupoid. Finally, we apply the previous construction to the formal derivation of the variational error for numerical integrators of forced Euler-Poincaré equations and the application of this theory to the derivation of geometric integrators for forced systems.</description><subject>Euler-Poincaré equations</subject><subject>forced systems</subject><subject>geometric integration</subject><subject>variational integrators</subject><issn>0951-7715</issn><issn>1361-6544</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><recordid>eNp1kLFOwzAQhi0EEqWwM3phI-1d7CbOiKoClSrBAAws1iV2iqs2LnYq1EfiOXgx0hYxwXA66fT9v3QfY5cIAwSlhigyTLKRlEMqVVniEev9no5ZD4oRJnmOo1N2FuMCAFGlosdeXyg4ap1vaMl9MDbw2u-nsobPaB6omTtqeNzG1q4in04HfLJZ2pA8etdUFL4-uX3f7Csi_3Dt2z7smvk5O6lpGe3Fz-6z59vJ0_g-mT3cTcc3s6QSCG2CMrcmLchSamol6zTLoLC5siVIUAYBUqjKCpQ0pSSBtlKWsKRUdrhBFH0Gh94q-BiDrfU6uBWFrUbQOzd6J0LvROiDmy5ydYg4v9YLvwnd91E3vtFCaKVFDoVem7rjrv_g_q39BlJmdLc</recordid><startdate>20200801</startdate><enddate>20200801</enddate><creator>Martín de Diego, D</creator><creator>Martín de Almagro, R T Sato</creator><general>IOP Publishing</general><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0001-6762-8909</orcidid></search><sort><creationdate>20200801</creationdate><title>Variational order for forced Lagrangian systems II. Euler-Poincaré equations with forcing</title><author>Martín de Diego, D ; Martín de Almagro, R T Sato</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c310t-147ed29aea2df84f26609e78eb0408d10020cbc084db4a31ec8ea1ba24df8d113</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Euler-Poincaré equations</topic><topic>forced systems</topic><topic>geometric integration</topic><topic>variational integrators</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Martín de Diego, D</creatorcontrib><creatorcontrib>Martín de Almagro, R T Sato</creatorcontrib><collection>CrossRef</collection><jtitle>Nonlinearity</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Martín de Diego, D</au><au>Martín de Almagro, R T Sato</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Variational order for forced Lagrangian systems II. Euler-Poincaré equations with forcing</atitle><jtitle>Nonlinearity</jtitle><stitle>Non</stitle><addtitle>Nonlinearity</addtitle><date>2020-08-01</date><risdate>2020</risdate><volume>33</volume><issue>8</issue><spage>3709</spage><epage>3738</epage><pages>3709-3738</pages><issn>0951-7715</issn><eissn>1361-6544</eissn><coden>NONLE5</coden><abstract>In this paper we provide a variational derivation of the Euler-Poincaré equations for systems subjected to external forces using an adaptation of the techniques introduced by Galley and others Martín de Diego and Martín de Almagro (2018 Nonlinearity 31 3814-3846), Galley (2013 Phys. Rev. Lett. 110 174301), Galley et al (2014 (arXiv:[math-Ph] 1412.3082)). Moreover, we study in detail the underlying geometry which is related to the notion of Poisson groupoid. Finally, we apply the previous construction to the formal derivation of the variational error for numerical integrators of forced Euler-Poincaré equations and the application of this theory to the derivation of geometric integrators for forced systems.</abstract><pub>IOP Publishing</pub><doi>10.1088/1361-6544/ab8bb1</doi><tpages>3738</tpages><orcidid>https://orcid.org/0000-0001-6762-8909</orcidid></addata></record> |
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subjects | Euler-Poincaré equations forced systems geometric integration variational integrators |
title | Variational order for forced Lagrangian systems II. Euler-Poincaré equations with forcing |
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