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Accurate conserved quantity and approximate conserved quantity deduced from Noether symmetry of Lagrange equations for a weakly Chetaev nonholonomic system were studied. First, the differential equations of motion of the system were established. Second, under the infinitesimal transformations of group, the definitions of Noether symmetry for the weakly Chetaev nonholonomic system and the first approximate system were given. Third, the first approximate Noether equation was mainly obtained, and the expressions of the accurate and approximate conserved quantities were deduced from the Noether symmetry for the weakly Chetaev nonholonomic system. Finally, an example was given to illustrate the application of the results.

Conformal invariance and conserved quantity of Mei symmetry for Appell equations of nonholonomic system of Chetaev's type with variable mass are studied. The conformal invariance and Mei symmetry for Appell equations of nonholonomic systems of Chetaev's type with variable mass are defined under the infinitesimal transformation of group, and the determining equations of conformal invariance of Mei symmetry for the system are given. Then, the expression of the corresponding conserved quantity of the system is derived. Finally, an example is given to illustrate the application of the results.