Noether symmetry of multi-delay Birkhoffian system and its conserved quantity
The Birkhoffian system, an important mechanical system in analytical mechanics, is studied in the background of multiple time delays. Both the multi-delay Birkhoffian system and the Hamiltonian system are investigated. First, the more general framework is discussed. The Pfaff–Birkhoff action is pres...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
AIP Publishing LLC
2025-01-01
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| Series: | AIP Advances |
| Online Access: | http://dx.doi.org/10.1063/5.0242244 |
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| Summary: | The Birkhoffian system, an important mechanical system in analytical mechanics, is studied in the background of multiple time delays. Both the multi-delay Birkhoffian system and the Hamiltonian system are investigated. First, the more general framework is discussed. The Pfaff–Birkhoff action is presented with multiple time delays. The multi-delay differential equations of motion are derived for both Birkhoffian and Hamiltonian models. Second, the invariance and two different kinds of Noether symmetries of the multi-delay Pfaff action are studied. Third, due to the effects of different time delays, the corresponding Noether-type theorems of multi-delay Birkhoffian systems are obtained. Two examples are presented to demonstrate the applications of the results. |
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| ISSN: | 2158-3226 |