Non-Noether Symmetrical Conserved Quantity for Nonholonomic Mechanical Systems with Variable Mass

Using the Lie symmetry under infinitesimal transformations in which the time is not variable,we studied a new conserved quantity for the nonholonomic mechanical systems with a variable mass. The differential equations of the systems and the determining equations of Lie symmetry under infinitesimal transformations are given. The Hojman's conservation theorems of the systems are established.Finally, we give an example to illustrate the application of the result.