This paper studies two new types of conserved quantities deduced by Noether–Mei symmetry of mechanical system in phase space. The definition and criterion of Noether–Mei symmetry for the system are given. A coordination function is introduced, and the conditions under which the Noether–Mei symmetry leads to the two types of conserved quantities and the forms of the two types of conserved quantities are obtained. An illustrative example is given. The coordination function can be selected according to the demand for finding the gauge function, and the choice of the coordination function has multiformity, so more conserved quantities deduced from Noether–Mei symmetry of mechanical system can be obtained.
A kind of conserved quantity which directly results from the Mei symmetry of general holonomic mechanical system is studied in the paper. The definition and criterion of Mei symmetry for the general holonomic mechanical system are given. The conditions under which Mei symmetry can lead to a conserved quantity and the form of the conserved quantity are deduced. An example is given to illustrate the application of the result.
Two types of conserved quantities deduced by Lie-Mei symmetry of variable mass mechanical system are studied in phase space in the paper. The definition and criterion of Lie-Mei symmetry for the system are given. A coordination function is introduced,and the conditions under which the Lie-Mei symmetry leads to the two types of conserved quantities and the forms of the two types of conserved quantities are obtained. An illustrative example is given. The coordination function can be selected according to the requirement for finding the gauge function,and the choice of the coordination function is multiformal,so more conserved quantities can be deduced from Lie-Mei symmetry of the system.
Two new types of conserved quantities deduced by Noether-Mei symmetry of nonholonomic mechanical system are studied. The definition and criterion of Noether-Mei symmetry for the system are given. A coordination function is introduced, and the conditions under which the Noether-Mei symmetry leads to the two types of conserved quantities and the forms of the two types of conserved quantities are obtained. An illustrative example is given. The coordination function can be selected according to the demand for finding the gauge function, and the choice of the coordination function has multiformity, so more conserved quantities deduced from Noether-Mei symmetry of mechanical system can be obtained.
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