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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.

In this study, the effects of Ti and Ce on the microstructure, corrosion behavior and rust resistance of invar alloys were investigated in detail. The precipitation phase which can be used as the core of heterogeneous nucleation can be formed by adding an appropriate amount of Ti and Ce, which promotes microstructure refinement and homogenization of the invar alloy. Moreover, the electrochemical behavior of invar alloys with different Ti and Ce contents was studied. The results show that with the addition of alloying elements, the self-corrosion potential of the alloy becomes positive, and the self-corrosion current decreases, indicating that the addition of Ti and Ce is beneficial for improving the corrosion properties of the alloy. This is primarily because Ti and Ce combine easily with unfavorable elements to form precipitates, which reduces the factors affecting the corrosion resistance of the alloy. The invar alloy with superior corrosion resistance was selected for the dipping test. X-ray diffraction analysis showed that the addition of Ti and Ce increased the amount of α-FeOOH and enhanced the protective effect of the antirust layer.

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