The perturbation to Noether symmetry and adiabatic invariants for dynamical systems with nonstandard Lagrangians are studied.Based on two kinds of nonstandard Lagrangians(i.e.exponential Lagrangians and power-law Lagr...The perturbation to Noether symmetry and adiabatic invariants for dynamical systems with nonstandard Lagrangians are studied.Based on two kinds of nonstandard Lagrangians(i.e.exponential Lagrangians and power-law Lagrangians),the exact invariants of Noether type are given.Based on the definition of highorder adiabatic invariants,the relationship between the perturbation of Noether symmetry and the adiabatic invariants of the system under a small disturbance is studied,and then the corresponding theorems of adiabatic invariants are established.Finally,two examples are given to illustrate the methods and results appear in this paper.展开更多
In this paper, Noether's theorem and its inverse theorem are proved for the fractional variational problems based on logarithmic Lagrangian systems. The Hamilton principle of the systems is derived. And the defini...In this paper, Noether's theorem and its inverse theorem are proved for the fractional variational problems based on logarithmic Lagrangian systems. The Hamilton principle of the systems is derived. And the definitions and the criterions of Noether's symmetry and Noether's quasi-symmetry of the systems based on logarithmic Lagrangians are given. The intrinsic relation between Noether's symmetry and the conserved quantity is established. At last an example is given to illustrate the application of the results.展开更多
基金National Natural Science Foundations of China(Nos.11572212,11272227)Innovation Program for Postgraduate of Suzhou University of Science and Technology,China(No.SKCX15_062)
文摘The perturbation to Noether symmetry and adiabatic invariants for dynamical systems with nonstandard Lagrangians are studied.Based on two kinds of nonstandard Lagrangians(i.e.exponential Lagrangians and power-law Lagrangians),the exact invariants of Noether type are given.Based on the definition of highorder adiabatic invariants,the relationship between the perturbation of Noether symmetry and the adiabatic invariants of the system under a small disturbance is studied,and then the corresponding theorems of adiabatic invariants are established.Finally,two examples are given to illustrate the methods and results appear in this paper.
基金Supported by the National Natural Science Foundation of China(61473338)Hubei Province Key Laboratory of Systems Science in Metallurgical Process(Wuhan University of Science and Technology)(Y201514)
文摘In this paper, Noether's theorem and its inverse theorem are proved for the fractional variational problems based on logarithmic Lagrangian systems. The Hamilton principle of the systems is derived. And the definitions and the criterions of Noether's symmetry and Noether's quasi-symmetry of the systems based on logarithmic Lagrangians are given. The intrinsic relation between Noether's symmetry and the conserved quantity is established. At last an example is given to illustrate the application of the results.
