In this paper, we investigate whether the Lie symmetry can induce the Mei conserved quantity directly in a nonconservative Hamilton system and a theorem is presented. The condition under which the Lie symmetry of the system directly induces the Mei conserved quantity is given. Meanwhile, an example is discussed to illustrate the application of the results. The present results have shown that the Lie symmetry of a nonconservative Hamilton system can also induce the Mei conserved quantity directly.
This paper studies the Noether symmetry and Mei symmetry of a discrete holonomic mechanical system with variable mass. Firstly, by the difference discrete variation approach, the discrete equations of motion of the system are established. Secondly, the definitions of Noether symmetry and Mei symmetry are given, and the conditions under which the Noether conserved quantity can be induced by Noether symmetry and Mei symmetry are obtained. Finally, an example is discussed to illustrate these results.
In this paper the Lie symmetry and Noether conserved quantity of a discrete difference sequence Hamilton system with variable mass are studied. Firstly, the difference dynamical equations of the discrete difference sequence Hamilton system with variable mass are built. Secondly, the determining equations and the definition of Lie symmetry for difference dynamical equations of the discrete difference sequence Hamilton system under infinitesimal transformation groups are given. Thirdly, the forms and conditions of Noether conserved quantities to which Lie symmetries will lead in a discrete mechanical system are obtained. Finally, an example is given to illustrate the application of the results.
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