A variational approach to the analysis of dissipative electromechanical systems.
We develop a method for systematically constructing Lagrangian functions for dissipative mechanical, electrical, and electromechanical systems. We derive the equations of motion for some typical electromechanical systems using deterministic principles that are strictly variational. We do not use any...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Public Library of Science (PLoS)
2014-01-01
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| Series: | PLoS ONE |
| Online Access: | http://europepmc.org/articles/PMC3938407?pdf=render |
| _version_ | 1818424687684747264 |
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| author | Andrew Allison Charles E M Pearce Derek Abbott |
| author_facet | Andrew Allison Charles E M Pearce Derek Abbott |
| author_sort | Andrew Allison |
| collection | DOAJ |
| description | We develop a method for systematically constructing Lagrangian functions for dissipative mechanical, electrical, and electromechanical systems. We derive the equations of motion for some typical electromechanical systems using deterministic principles that are strictly variational. We do not use any ad hoc features that are added on after the analysis has been completed, such as the Rayleigh dissipation function. We generalise the concept of potential, and define generalised potentials for dissipative lumped system elements. Our innovation offers a unified approach to the analysis of electromechanical systems where there are energy and power terms in both the mechanical and electrical parts of the system. Using our novel technique, we can take advantage of the analytic approach from mechanics, and we can apply these powerful analytical methods to electrical and to electromechanical systems. We can analyse systems that include non-conservative forces. Our methodology is deterministic, and does does require any special intuition, and is thus suitable for automation via a computer-based algebra package. |
| first_indexed | 2024-12-14T14:02:00Z |
| format | Article |
| id | doaj.art-5c475e2d3fe946569e1550cbb6186e3c |
| institution | Directory Open Access Journal |
| issn | 1932-6203 |
| language | English |
| last_indexed | 2024-12-14T14:02:00Z |
| publishDate | 2014-01-01 |
| publisher | Public Library of Science (PLoS) |
| record_format | Article |
| series | PLoS ONE |
| spelling | doaj.art-5c475e2d3fe946569e1550cbb6186e3c2022-12-21T22:58:42ZengPublic Library of Science (PLoS)PLoS ONE1932-62032014-01-0192e7719010.1371/journal.pone.0077190A variational approach to the analysis of dissipative electromechanical systems.Andrew AllisonCharles E M PearceDerek AbbottWe develop a method for systematically constructing Lagrangian functions for dissipative mechanical, electrical, and electromechanical systems. We derive the equations of motion for some typical electromechanical systems using deterministic principles that are strictly variational. We do not use any ad hoc features that are added on after the analysis has been completed, such as the Rayleigh dissipation function. We generalise the concept of potential, and define generalised potentials for dissipative lumped system elements. Our innovation offers a unified approach to the analysis of electromechanical systems where there are energy and power terms in both the mechanical and electrical parts of the system. Using our novel technique, we can take advantage of the analytic approach from mechanics, and we can apply these powerful analytical methods to electrical and to electromechanical systems. We can analyse systems that include non-conservative forces. Our methodology is deterministic, and does does require any special intuition, and is thus suitable for automation via a computer-based algebra package.http://europepmc.org/articles/PMC3938407?pdf=render |
| spellingShingle | Andrew Allison Charles E M Pearce Derek Abbott A variational approach to the analysis of dissipative electromechanical systems. PLoS ONE |
| title | A variational approach to the analysis of dissipative electromechanical systems. |
| title_full | A variational approach to the analysis of dissipative electromechanical systems. |
| title_fullStr | A variational approach to the analysis of dissipative electromechanical systems. |
| title_full_unstemmed | A variational approach to the analysis of dissipative electromechanical systems. |
| title_short | A variational approach to the analysis of dissipative electromechanical systems. |
| title_sort | variational approach to the analysis of dissipative electromechanical systems |
| url | http://europepmc.org/articles/PMC3938407?pdf=render |
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