Noether symmetry and conserved quantity for a weakly nonholonomic system on time scales

This paper mainly investigated Noether symmetry and conserved quantity for a weakly nonholonomic system on time scales. Firstly, we provided the differential equations of motion for the first-order approximate system corresponding to the weakly nonholonomic system. Secondly, we offered the definitions and criteria of Noether symmetry for the first-order approximate system of the weakly nonholonomic system. Then, the expressions of the approximate conserved quantity of Noether symmetry in weakly nonholonomic systems were obtained. Finally, an example was given to illustrate the application of the results.