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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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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| author | Xin-Yu Du Xiang-Hua Zhai |
| author_facet | Xin-Yu Du Xiang-Hua Zhai |
| author_sort | Xin-Yu Du |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-97ba4c31104847df8f339de47e6601f1 |
| institution | Kabale University |
| issn | 2158-3226 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | AIP Publishing LLC |
| record_format | Article |
| series | AIP Advances |
| spelling | doaj-art-97ba4c31104847df8f339de47e6601f12025-02-03T16:40:42ZengAIP Publishing LLCAIP Advances2158-32262025-01-01151015104015104-1810.1063/5.0242244Noether symmetry of multi-delay Birkhoffian system and its conserved quantityXin-Yu Du0Xiang-Hua Zhai1School of Mathematical Sciences, Suzhou University of Science and Technology, Suzhou 215009, ChinaCollege of Civil Engineering, Suzhou University of Science and Technology, Suzhou 215011, ChinaThe 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.http://dx.doi.org/10.1063/5.0242244 |
| spellingShingle | Xin-Yu Du Xiang-Hua Zhai Noether symmetry of multi-delay Birkhoffian system and its conserved quantity AIP Advances |
| title | Noether symmetry of multi-delay Birkhoffian system and its conserved quantity |
| title_full | Noether symmetry of multi-delay Birkhoffian system and its conserved quantity |
| title_fullStr | Noether symmetry of multi-delay Birkhoffian system and its conserved quantity |
| title_full_unstemmed | Noether symmetry of multi-delay Birkhoffian system and its conserved quantity |
| title_short | Noether symmetry of multi-delay Birkhoffian system and its conserved quantity |
| title_sort | noether symmetry of multi delay birkhoffian system and its conserved quantity |
| url | http://dx.doi.org/10.1063/5.0242244 |
| work_keys_str_mv | AT xinyudu noethersymmetryofmultidelaybirkhoffiansystemanditsconservedquantity AT xianghuazhai noethersymmetryofmultidelaybirkhoffiansystemanditsconservedquantity |