Conformal invariance for the nonholonomic constrained mechanical system of non-Chetaev's type

The conformal invariance and conserved quantity for the nonholonomic system of non-Chetaev's type are studied. Firstly, by introducing a one-parameter infinitesimal transformation group and its infinitesimal generator vector, the definition of conformal invariance and determining equation for the holonomic system which corresponds to a nonholonomic system of non-Chetaev's type are provided, and the relationship between the system's conformal invariance and Lie symmetry are discussed. Secondly, the conformal invariance of weak and strong Lie symmetry for the nonholonomic system of non-Chetaev's type is given using restriction equations and additional restriction equations. Thirdly, the system's corresponding conserved quantity is derived with the aid of a structure equation that the gauge function satisfies. Lastly, an example is given to illustrate the application of the method and its result.