Conformal invariance and conserved quantity of Mei symmetry for the nonholonomic system of Chetaev's type

For a nonholonomic system of Chetaev's type, the conformal invariance and the conserved quantity are studied. By the infinitesimal one-parameter transformation group and the infinitesimal generator vector, the definition of conformal invariance of Mei symmetry and the determining equation for the holonomic system which corresponds to a nonholonomic system are provided, and the relationship between the system conformal invariance and Mei symmetry is discussed. Using the restriction equations and the additional restriction equations, the conformal invariances of weak and strong Mei symmetrys for the system are given. With the aid of a structure equation that gauge function satisfies, the system corresponding conserved quantity is derived. Finally, an example is given to illustrate the application of the result.