Metriplectic Euler-Poincaré equations: smooth and discrete dynamics
In this paper we will introduce a discrete version of systems obtained by modifications of the Euler-Poincaré equations when we add a special type of dissipative force, so that the equations of motion can be described using the metriplectic formalism. The metriplectic representation of the dynamics...
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| Format: | Article |
| Language: | English |
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AIMS Press
2024-12-01
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| Series: | Communications in Analysis and Mechanics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/cam.2024040 |
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| author | Anthony Bloch Marta Farré Puiggalí David Martín de Diego |
| author_facet | Anthony Bloch Marta Farré Puiggalí David Martín de Diego |
| author_sort | Anthony Bloch |
| collection | DOAJ |
| description | In this paper we will introduce a discrete version of systems obtained by modifications of the Euler-Poincaré equations when we add a special type of dissipative force, so that the equations of motion can be described using the metriplectic formalism. The metriplectic representation of the dynamics allows us to describe the conservation of energy, as well as to guarantee entropy production. For deriving the discrete equations we use discrete gradients to numerically simulate the evolution of the continuous metriplectic equations preserving their main properties: preservation of energy and correct entropy production rate. |
| format | Article |
| id | doaj-art-ea377b9f267849caa2e7bc9436560c7a |
| institution | Kabale University |
| issn | 2836-3310 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Communications in Analysis and Mechanics |
| spelling | doaj-art-ea377b9f267849caa2e7bc9436560c7a2025-01-23T07:55:56ZengAIMS PressCommunications in Analysis and Mechanics2836-33102024-12-0116491092710.3934/cam.2024040Metriplectic Euler-Poincaré equations: smooth and discrete dynamicsAnthony Bloch0Marta Farré Puiggalí1David Martín de Diego2Department of Mathematics, University of Michigan 530 Church Street, Ann Arbor, MI, USAInstituto de Ciencias Matemáticas, ICMAT (CSIC-UAM-UC3M-UCM) Madrid, SpainInstituto de Ciencias Matemáticas, ICMAT (CSIC-UAM-UC3M-UCM) Madrid, SpainIn this paper we will introduce a discrete version of systems obtained by modifications of the Euler-Poincaré equations when we add a special type of dissipative force, so that the equations of motion can be described using the metriplectic formalism. The metriplectic representation of the dynamics allows us to describe the conservation of energy, as well as to guarantee entropy production. For deriving the discrete equations we use discrete gradients to numerically simulate the evolution of the continuous metriplectic equations preserving their main properties: preservation of energy and correct entropy production rate.https://www.aimspress.com/article/doi/10.3934/cam.2024040metriplectic systempoisson manifolddiscrete gradienteuler-poincaréequations |
| spellingShingle | Anthony Bloch Marta Farré Puiggalí David Martín de Diego Metriplectic Euler-Poincaré equations: smooth and discrete dynamics Communications in Analysis and Mechanics metriplectic system poisson manifold discrete gradient euler-poincaréequations |
| title | Metriplectic Euler-Poincaré equations: smooth and discrete dynamics |
| title_full | Metriplectic Euler-Poincaré equations: smooth and discrete dynamics |
| title_fullStr | Metriplectic Euler-Poincaré equations: smooth and discrete dynamics |
| title_full_unstemmed | Metriplectic Euler-Poincaré equations: smooth and discrete dynamics |
| title_short | Metriplectic Euler-Poincaré equations: smooth and discrete dynamics |
| title_sort | metriplectic euler poincare equations smooth and discrete dynamics |
| topic | metriplectic system poisson manifold discrete gradient euler-poincaréequations |
| url | https://www.aimspress.com/article/doi/10.3934/cam.2024040 |
| work_keys_str_mv | AT anthonybloch metriplecticeulerpoincareequationssmoothanddiscretedynamics AT martafarrepuiggali metriplecticeulerpoincareequationssmoothanddiscretedynamics AT davidmartindediego metriplecticeulerpoincareequationssmoothanddiscretedynamics |