中文摘要：

研究了时间尺度上Nabla变分问题的非完整力学系统的Noether理论。根据时间尺度上的微积分理论和Delta导数与Nabla导数之间关系，建立了时间尺度上Nabla导数的非完整Lagrange方程。根据时间尺度上Nabla变分问题的Hamilton作用量在无限小变换下的变换性质，建立了Nabla变分问题的非完整力学系统的Noether等式，并找到了相应的守恒量。最后，举例说明结果的应用。

英文摘要：

The Noether theorem for nonholonomic mechanical systems of Nabla variational problem on time scales is studied.Firstly,based on the relationship between the Delta calculus and the Nabla calcu-lus on time scales and the theory of time scale,the nonholonomic Lagrange equation for Nabla variational problem on time scales is established.Secondly,according to invariance of the Hamilton action under the infinitesimal transformation of Nabla variational problem on time scales,the Noether identity for nonholo-nomic mechanical systems is established,and the corresponding Noether conserved quantity is obtained. Finally,an example is presented to illustrate the application of the results.