IJcken, Martin van (2023) UNIFYING THE DESCRIPTION OF FREE SYSTEMS WITH LIE GROUP ANALYSIS. Bachelor's Thesis, Mathematics.
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Abstract
This paper unifies rigid bodies and fluid flow through Lie group analysis. By exploiting similarities in the symmetries of their Lagrangian, the study reveals that their behavior can be seen as geodesic motion on their respective configuration spaces when an appropriate metric is chosen. Using the Euler-Poincaré reduction theorem, the Euler-Arnold equations for rigid bodies and fluids are derived. Additionally, different systems described by Lie group analysis with various groups and metrics are mentioned, demonstrating the framework's versatility. The behavior of the Hopf/inviscid Burgers' equation and the Euler ideal flow equation is derived, confirming their adherence to the Lie group analysis framework.
| Item Type: | Thesis (Bachelor's Thesis) |
|---|---|
| Supervisor name: | Veen, R.I. van der and Roest, D. |
| Degree programme: | Mathematics |
| Thesis type: | Bachelor's Thesis |
| Language: | English |
| Date Deposited: | 17 Jul 2023 10:24 |
| Last Modified: | 17 Jul 2023 10:24 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/30661 |
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