The new variational principle of Gauss's form of nonlinear nonholonomic nonpotential system relative to non-inertial reference frame is established by constructing generalized inertial potentials. Naether's th...The new variational principle of Gauss's form of nonlinear nonholonomic nonpotential system relative to non-inertial reference frame is established by constructing generalized inertial potentials. Naether's theorem and Naether's inverse theorem of the system above is presented and proved. Finally, one example is given to illustrate the application.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
文摘The new variational principle of Gauss's form of nonlinear nonholonomic nonpotential system relative to non-inertial reference frame is established by constructing generalized inertial potentials. Naether's theorem and Naether's inverse theorem of the system above is presented and proved. Finally, one example is given to illustrate the application.
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.
