A fractional variational approach for modelling dissipative mechanical systems: continuous and discrete settings
Employing a phase space which includes the (Riemann-Liouville) fractional derivative of curves evolving on real space, we develop a restricted variational principle for Lagrangian systems yielding the so-called restricted fractional Euler-Lagrange equations (both in the continuous and discrete setti...
| Hlavní autoři: | , |
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| Médium: | Journal article |
| Jazyk: | English |
| Vydáno: |
Elsevier
2018
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| _version_ | 1826297615812132864 |
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| author | Jimenez, F Ober-Blobaum, S |
| author_facet | Jimenez, F Ober-Blobaum, S |
| author_sort | Jimenez, F |
| collection | OXFORD |
| description | Employing a phase space which includes the (Riemann-Liouville) fractional derivative of curves evolving on real space, we develop a restricted variational principle for Lagrangian systems yielding the so-called restricted fractional Euler-Lagrange equations (both in the continuous and discrete settings), which, as we show, are invariant under linear change of variables. This principle relies on a particular restriction upon the admissible variation of the curves. In the case of the half-derivative and mechanical Lagrangians, i.e. kinetic minus potential energy, the restricted fractional Euler-Lagrange equations model a dissipative system in both directions of time, summing up to a set of equations that is invariant under time reversal. Finally, we show that the discrete equations are a meaningful discretisation of the continuous ones. |
| first_indexed | 2024-03-07T04:34:21Z |
| format | Journal article |
| id | oxford-uuid:cf6fd21d-f307-45eb-bfb6-336f48cd036c |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T04:34:21Z |
| publishDate | 2018 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | oxford-uuid:cf6fd21d-f307-45eb-bfb6-336f48cd036c2022-03-27T07:42:25ZA fractional variational approach for modelling dissipative mechanical systems: continuous and discrete settingsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:cf6fd21d-f307-45eb-bfb6-336f48cd036cEnglishSymplectic ElementsElsevier2018Jimenez, FOber-Blobaum, SEmploying a phase space which includes the (Riemann-Liouville) fractional derivative of curves evolving on real space, we develop a restricted variational principle for Lagrangian systems yielding the so-called restricted fractional Euler-Lagrange equations (both in the continuous and discrete settings), which, as we show, are invariant under linear change of variables. This principle relies on a particular restriction upon the admissible variation of the curves. In the case of the half-derivative and mechanical Lagrangians, i.e. kinetic minus potential energy, the restricted fractional Euler-Lagrange equations model a dissipative system in both directions of time, summing up to a set of equations that is invariant under time reversal. Finally, we show that the discrete equations are a meaningful discretisation of the continuous ones. |
| spellingShingle | Jimenez, F Ober-Blobaum, S A fractional variational approach for modelling dissipative mechanical systems: continuous and discrete settings |
| title | A fractional variational approach for modelling dissipative mechanical systems: continuous and discrete settings |
| title_full | A fractional variational approach for modelling dissipative mechanical systems: continuous and discrete settings |
| title_fullStr | A fractional variational approach for modelling dissipative mechanical systems: continuous and discrete settings |
| title_full_unstemmed | A fractional variational approach for modelling dissipative mechanical systems: continuous and discrete settings |
| title_short | A fractional variational approach for modelling dissipative mechanical systems: continuous and discrete settings |
| title_sort | fractional variational approach for modelling dissipative mechanical systems continuous and discrete settings |
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