中文摘要：

研究变质量相对运动力学系统Nielsen方程的Noether守恒量．在群的无限小变换下，给出变质量相对运动力学系统Nielsen方程Noether对称性的定义及Noether对称性的判据；进而得到与变质量相对运动力学系统Nielsen方程Noether对称性相应的Noether守恒量．举例说明结果的应用．

英文摘要：

Noether conserved quantity for Nielsen equations in a variable mass dynamical system of the rela- tive motion has been studied. The definition and criteria of Noether symmetry for the Nielsen equations in the sys- tem under the infinitesimal transformations of groups have been explored. Meanwhile the Noether conserved quan- tity corresponding to Noether symmetry for the Nielsen equations in the system has been obtained. Finally, an ex- ample has been given to illustrate the application of the results.