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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2401.05220 |
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| _version_ | 1866914637045301248 |
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| author | Bloch, Anthony Puiggalí, Marta Farré de Diego, David Martín |
| author_facet | Bloch, Anthony Puiggalí, Marta Farré de Diego, David Martín |
| contents | In this paper we will study some interesting properties of 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. Moreover, we describe the use of discrete gradient systems to numerically simulate the evolution of the continuous metriplectic equations preserving their main properties: preservation of energy and correct entropy production rate. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_05220 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Metriplectic Euler-Poincaré equations: smooth and discrete dynamics Bloch, Anthony Puiggalí, Marta Farré de Diego, David Martín Mathematical Physics Dynamical Systems 70G45, 37J37 In this paper we will study some interesting properties of 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. Moreover, we describe the use of discrete gradient systems to numerically simulate the evolution of the continuous metriplectic equations preserving their main properties: preservation of energy and correct entropy production rate. |
| title | Metriplectic Euler-Poincaré equations: smooth and discrete dynamics |
| topic | Mathematical Physics Dynamical Systems 70G45, 37J37 |
| url | https://arxiv.org/abs/2401.05220 |