Variational integrators for dissipative systems
This paper uses physical arguments to derive variational integration schemes for dissipative mechanical systems. These integration algorithms find utility in the solution of the equations of motion and optimal control problems for these systems. Engineers usually represent dissipation effects using...
| Main Authors: | , , |
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| Format: | Journal article |
| Language: | English |
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Institute of Electrical and Electronics Engineers
2020
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| _version_ | 1797074351503179776 |
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| author | Limebeer, D Ober-Blobaum, S Haddad-Farshi, F |
| author_facet | Limebeer, D Ober-Blobaum, S Haddad-Farshi, F |
| author_sort | Limebeer, D |
| collection | OXFORD |
| description | This paper uses physical arguments to derive variational integration schemes for dissipative mechanical systems.
These integration algorithms find utility in the solution of the equations of motion and optimal control problems for these systems. Engineers usually represent dissipation effects using phenomenological devices such as ‘dampers’. In the work presented here we replace these dampers with a lossless transmissionline in order that the equations of motion are derivable from a variational principle. The associated system Lagrangian can then be discretized and used to develop low-order variational integration schemes that inherit the advantageous features of their conservative counterparts. The properties of a lossless spring-inerter based transmission system are analyzed in detail, with the resulting variational integration schemes shown to have excellent numerical properties. The paper concludes with the analysis of a dissipative variant of the classical Kepler central force problem.
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| first_indexed | 2024-03-06T23:34:52Z |
| format | Journal article |
| id | oxford-uuid:6d51e03a-d032-4911-a756-7d17c7f018ef |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T23:34:52Z |
| publishDate | 2020 |
| publisher | Institute of Electrical and Electronics Engineers |
| record_format | dspace |
| spelling | oxford-uuid:6d51e03a-d032-4911-a756-7d17c7f018ef2022-03-26T19:16:59ZVariational integrators for dissipative systemsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:6d51e03a-d032-4911-a756-7d17c7f018efEnglishSymplectic ElementsInstitute of Electrical and Electronics Engineers2020Limebeer, DOber-Blobaum, SHaddad-Farshi, FThis paper uses physical arguments to derive variational integration schemes for dissipative mechanical systems. These integration algorithms find utility in the solution of the equations of motion and optimal control problems for these systems. Engineers usually represent dissipation effects using phenomenological devices such as ‘dampers’. In the work presented here we replace these dampers with a lossless transmissionline in order that the equations of motion are derivable from a variational principle. The associated system Lagrangian can then be discretized and used to develop low-order variational integration schemes that inherit the advantageous features of their conservative counterparts. The properties of a lossless spring-inerter based transmission system are analyzed in detail, with the resulting variational integration schemes shown to have excellent numerical properties. The paper concludes with the analysis of a dissipative variant of the classical Kepler central force problem. |
| spellingShingle | Limebeer, D Ober-Blobaum, S Haddad-Farshi, F Variational integrators for dissipative systems |
| title | Variational integrators for dissipative systems |
| title_full | Variational integrators for dissipative systems |
| title_fullStr | Variational integrators for dissipative systems |
| title_full_unstemmed | Variational integrators for dissipative systems |
| title_short | Variational integrators for dissipative systems |
| title_sort | variational integrators for dissipative systems |
| work_keys_str_mv | AT limebeerd variationalintegratorsfordissipativesystems AT oberblobaums variationalintegratorsfordissipativesystems AT haddadfarshif variationalintegratorsfordissipativesystems |