Unified symmetry of nonholonomic mechanical systems with variable mass

Based on the total timederivative along the trajectory of the systemthe definition and the criterion for a unified symmetry of nonholonomicmechanical system with variable mass are presented in this paper. A newconserved quantity, aswell as the Noether conserved quantity and the Hojman conserved quantity,deduced from the unified symmetry, are also obtained. An example is given toillustrate the application of the results.