完整系统形式不变性导致的新守恒量

New Conserved Quantity Constructed upon Form Invariance for Holonomic Systems

  • 摘要: 研究完整力学系统由形式不变性直接导出的新型守恒量.用双面理想完整约束力学系统的运动微分方程在无限小变换下的形式不变性,给出系统形式不变性的定义和判据.得到形式不变性导致守恒量的条件以及守恒量的形式,并给出三个特殊情形下的推论.举例说明结果的应用.

     

    Abstract: A new conserved quantity constructed directly using the form invariance for a holonomic system is presented. The definition and criterion of the form invariance of the system are obtained relying upon the fact that the differential equations of motion of the mechanical system with bilateral ideal holonomic constraints preserve an invariance under infinitesimal transformations. The condition under which the form invariance can lead to a conserved quantity and the form of the conservsd quantity are deduced,and three corollaries in special cases are given. Two examples are given to illustrate the application of the results.

     

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