变质量力学系统Nielsen方程的形式不变性

Form Invariance of the Nielsen Equation of Variable Mass Mechanical System

力学系统对称性与守恒量的研究在数学、力学、物理学中都具有非常重要的意义。力学系统的对称性与守恒量的近代理论主要有Noether对称性理论和Lie对称性理论。形式不变性是不同于Noether对称性和Lie对称性的一种新的对称性理论。本文研究变质量力学系统Nielsen方程的形式不变性 ,给出变质量保守力学系统Nielsen方程的形式不变性的定义和判据 ,研究形式不变性和Noether对称性的关系 。

Study of the symmetry and conserved quantity has its very important significance in mathematics, mechanics and physics. Modern theories of the symmetry and conserved quantity of a mechanical system can chiefly be listed as belonging to the Noether symmetry theory and Lie symmetry theory. Form invariance is a new theory of symmetry that differs from the Noether symmetry and the Lie symmetry. In this paper, the form invariance of Nielsen equation for variable mass conservative mechanical system was studied. The definition and criterion of form invariance of Nielsen equation for variable mass conservative mechanical systems were given. The relation between the form invariance and the Noether symmetry was studied. An example was given to illustrate the application of the result.