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
基金supported by the National Natural Science Foundations of China (Nos. 11972241,11572212,11272227)the Natural Science Foundation of Jiangsu Province(No. BK20191454).
文摘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.
