Affiliation:
1. College of Civil Engineering, Suzhou University of Science and Technology, Suzhou 215011, China
Abstract
The study of multi-time-delay dynamical systems has highlighted many challenges, especially regarding the solution and analysis of multi-time-delay equations. The symmetry and conserved quantity are two important and effective essential properties for understanding complex dynamical behavior. In this study, a multi-time-delay non-conservative mechanical system is investigated. Firstly, the multi-time-delay Hamilton principle is proposed. Then, multi-time-delay non-conservative dynamical equations are deduced. Secondly, depending on the infinitesimal group transformations, the invariance of the multi-time-delay Hamilton action is studied, and Noether symmetry, Noether quasi-symmetry, and generalized Noether quasi-symmetry are discussed. Finally, Noether-type conserved quantities for a multi-time-delay Lagrangian system and a multi-time-delay non-conservative mechanical system are obtained. Two examples in terms of a multi-time-delay non-conservative mechanical system and a multi-time-delay Lagrangian system are given.
Funder
National Natural Science Foundation of China
Reference46 articles.
1. Review on nonlinear dynamic systems involving time delays;Hu;Adv. Mech.,1999
2. Time-delay systems: An overview of some recent advances and open problems;Richard;Automatica,2003
3. Advances in dynamics for delayed systems;Xu;Adv. Mech.,2006
4. Singular perturbation methods for nonlinear dynamic systems with time delays;Hu;Chaos Solitons Fractals,2009
5. Time delay for the Dirac equation;Naumkin;Lett. Math. Phys.,2016