【摘要】 研究事件空间中完整力学系统由特殊Lie对称性、Noether对称性和形式不变性导致的Hojman守恒量 .列出系统的运动微分方程 .给出Lie对称性、Noether对称性和形式不变性的判据 ,以及三种对称性之间的关系 .将Hojman定理推广并应用于事件空间完整系统 ,得到非Noether守恒量 .举例说明结果的应用 .更多还原

【Abstract】 A Hojman conserved quantity constructed by using the special Lie symmetry, or the Noether symmetry, or the form invariance for a holonomic system in the event space is studied. First, the differential equations of motion of the system are established. Second, the critera of three kinds of symmetries, such as the Lie symmetry, the Noether symmetry and the form invariance, and the relation among them are obtained. Third, the conservation law theorem gained by Hojman is generalized and applied to the system, and a non Noether conserved quantity is obtained. Two examples are finally given to illustrate the application of the results.更多还原