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Recent Advances on Herglotz’s Generalized Variational Principle of Nonconservative Dynamics 被引量:5
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作者 ZHANG Yi 《Transactions of Nanjing University of Aeronautics and Astronautics》 EI CSCD 2020年第1期13-26,共14页
This paper summarized the recent development on Herglotz’s generalized variational principle and its symmetries and conserved quantities for nonconservative dynamical systems.Taking Lagrangian mechanics,Hamiltonian m... This paper summarized the recent development on Herglotz’s generalized variational principle and its symmetries and conserved quantities for nonconservative dynamical systems.Taking Lagrangian mechanics,Hamiltonian mechanics and Birkhoffian mechanics as three research frames,we introduce Herglotz’s generalized variational principle,dynamical equations of Herglotz type,Noether symmetry and conserved quantities,and their generalization to time-delay dynamics,fractional dynamics and time-scale dynamics,and put forward some problems as suggestions for future research. 展开更多
关键词 nonconservative dynamics herglotz’s generalized variational principle Lagrangian mechanics Hamil-tonian mechanics Birkhoffian mechanics
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Noether Theorem of Herglotz-Type for Nonconservative Hamilton Systems in Event Space 被引量:5
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作者 ZHANG Yi CAI Jinxiang 《Wuhan University Journal of Natural Sciences》 CAS CSCD 2021年第5期376-382,共7页
Focusing on the exploration of symmetry and conservation laws in event space, this paper studies Noether theorems of Herglotz-type for nonconservative Hamilton system. Herglotz’s generalized variational principle is ... Focusing on the exploration of symmetry and conservation laws in event space, this paper studies Noether theorems of Herglotz-type for nonconservative Hamilton system. Herglotz’s generalized variational principle is first extended to event space,and on this basis, Hamilton equations of Herglotz-type in event space are derived. The invariance of Hamilton-Herglotz action is then studied by introducing infinitesimal transformation, and the definition of Herglotz-type Noether symmetry in event space is given, and its criterion is derived. Noether theorem of Herglotz-type and its inverse for event space nonconservative Hamilton system are proved. The application of Herglotz-type Noether theorem we obtained is introduced by taking Emden-Fowler equation and linearly damped oscillator as examples. 展开更多
关键词 herglotz’s generalized variational principle Noether theorem nonconservative Hamilton system event space
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