Lie Symmetries and Non-Noether Conserved Quantities of Nonholonomic Systems

A new conservation theorem of the nonholonomic systems is studied. The conserved quantity is only constructed in terms of a general Lie group of transformation vector of the dynamical equations. Firstly, we establish the dynamical equations of the nonholonomic systems and the determining equations of Lie symmetry. Next, the theorem of non-Noether conserved quantity is deduced. Finally, we give an example to illustrate the application of the result.