In this paper,we study the form invariance and Noether symmetry of a relativistic mechanical system-Firstly,we give the Noether theorem of a relativistic mechanical system,and the definition and criterion and conserved quantity of the form invariance in the system-Next,the relation between the form invariance and Noether symmetry of the system is obtained-Finally,we give an example to illustrate the application of the result-
In this paper, the form invariance of nonconservative nonholonmic systems in the phase space is studied. The definition and criterion of the form invariance of nonholonmic nonconservative systems in the phase space is given.The structure equation and conservation law of form invariance is obtained.An example is given to illustrate the application of the result.
The Mei symmetry and the Lie symmetry of the relativistic Hamiltonian system are studied. The definition and criterion of the Mei symmetry and the Lie symmetry of the relativistic Hamiltonian system are given. The relationship between them is found. The conserved quantities which the Mei symmetry and the Lie symmetry lead to are obtained. An example is given to illustrate the application of the result.
We study the form invariance and Lie symmetry of a relativistic mechanical syste m. Firstly, we give the definition and criterion and conserved quantity of the f orm invariance and Lie symmetry in the system. Next, the relation between the fo rm invariance and Lie symmetry of the system is obtained. Finally, we give an ex ample to illustrate the application of the result.
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