Noether symmetry of multi-delay Birkhoffian system and its conserved quantity
Source abstract
Abstract
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.
Source: crossref · Quality: baseline
Research context
OpenAlex topics: Numerical methods for differential equations · Nonlinear Dynamics and Pattern Formation · Nonlinear Photonic Systems
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
Affiliations
School of Mathematical Sciences, Suzhou University of Science and Technology 1 , Suzhou 215009,
College of Civil Engineering, Suzhou University of Science and Technology 2 , Suzhou 215011,
Funding
National Natural Science Foundation of China
References (47)
Show source-provided references
1. Review on nonlinear dynamic systems involving time delays10.6052/1000-0992-1999-4-J1998-103 ↗
2. Time-delay systems: An overview of some recent advances and open problems10.1016/s0005-1098(03)00167-5 ↗
3. Advances in dynamics for delayed system
4. Singular perturbation methods for nonlinear dynamic systems with time delays10.1016/j.chaos.2007.07.048 ↗
5. Time delay for the Dirac equation10.1007/s11005-016-0871-5 ↗
6. Numerical study for a novel variable-order multiple time delay awareness programs mathematical model10.1016/j.apnum.2020.07.016 ↗
7. Predictor-based safety control for systems with multiple time-varying delays10.1016/j.ifacol.2022.11.330 ↗
8. Dynamics of fractional-order delay differential model for tumor-immune system10.1016/j.chaos.2019.109592 ↗
9. General stabilization approach of the low-order controller for both SISO systems and MIMO systems with multiple time delays10.1016/j.automatica.2024.111639 ↗
10. Analytical prediction of specific spatiotemporal patterns in nonlinear oscillator networks with distance-dependent time delays10.1103/physrevresearch.5.013159 ↗
11. 1964
12. Variational and optimal control problems with delayed argument10.1007/bf00927159 ↗
13. Conjugate-point conditions for variational problems with delayed argument10.1007/bf00932963 ↗
14. Systems with time delay in the calculus of variations: The method of steps10.1093/imamci/5.4.285 ↗
15. Sufficient conditions for variational problems with delayed argument10.1007/bf00952825 ↗
16. Sufficient conditions for optimal control problems with time delay10.1007/bf02192027 ↗
17. Optimal control of variational inequalities with delays in the highest order spatial derivatives10.1007/s10114-005-0688-0 ↗
18. Variational optimal-control problems with delayed arguments on time scales10.1155/2009/840386 ↗
19. Noether’s symmetry theorem for variational and optimal control problems with time delay10.3934/naco.2012.2.619 ↗
20. Herglotz’s variational problem for non-conservative system with delayed arguments under Lagrangian framework and its Noether’s theorem10.3390/sym12050845 ↗
21. Noether symmetry and conserved quantity for a Hamilton system with time delay10.1088/1674-1056/23/5/054501 ↗
22. Noether symmetries and conserved quantities for Birkhoffian systems with time delay10.1007/s11071-014-1274-8 ↗
23. Variational problems of Herglotz type with time delay: Dubois–Reymond condition and Noether’s first theorem10.3934/dcds.2015.35.4593 ↗
24. Higher-order variational problems of Herglotz type with time delay10.48550/arXiv.1603.04034 ↗
25. Linear or linearizable first-order delay ordinary differential equations and their lie point symmetries10.1088/1751-8121/aab3e9 ↗
26. Lagrangian formalism and Noether-type theorems for second-order delay ordinary differential equations10.1088/1751-8121/ace5f6 ↗
27. Higher-order Noether’s theorem for isoperimetric variational problems10.1007/s10957-023-02288-z ↗
28. Noether’s theorem for non-smooth extremals of variational problems with time delay10.1080/00036811.2012.762090 ↗
29. Constants of motion for isoperimetric variational problems with time delay10.1080/00036811.2020.1820995 ↗
30. Noether symmetries for non-conservative Lagrange systems with time delay based on fractional model10.1007/s11071-014-1734-1 ↗
31. Noether symmetries and conserved quantities for fractional Birkhoffian systems with time delay10.1016/j.cnsns.2015.11.020 ↗
32. Conservation laws for a delayed Hamiltonian system in a time scales version10.3390/sym10120668 ↗
33. Noether theorem for non-conservative systems with time delay on time scales10.1016/j.cnsns.2017.04.012 ↗
34. Optimal control with time delays via the penalty method10.1155/2014/250419 ↗
35. Noether symmetry of multi-time-delay non-conservative mechanical system and its conserved quantity10.3390/sym16040475 ↗
36. Herglotz type conservation laws for nonconservative nonholonomic systems10.1063/5.0170433 ↗
37. Symmetries and perturbations of time-scale nonshifted singular systems10.1063/5.0179739 ↗
38. Disturbation to lie symmetry for constrained Hamiltonian system within Agrawal’s operators10.1063/5.0187329 ↗
39. 1927
40. 1989
41. 1999
42. 1996
43. Theory of generalized canonical transformations for Birkhoff systems10.1155/2020/9482356 ↗
44. Geometric formulations and variational integrators of discrete autonomous Birkhoff systems10.1088/1674-1056/20/3/034501 ↗
45. Mei symmetry and new conserved quantities of time-scale Birkhoff’s equations10.1155/2020/1691760 ↗
46. Noether symmetry and conserved quantity for fractional Birkhoffian mechanics and its applications10.1515/fca-2018-0028 ↗
47. Structure-preserving algorithms for Birkhoffian systems10.1016/j.geomphys.2011.12.004 ↗