广义Chaplygin系统的Noether对称性

Noether Symmetry of Generalized Chaplygin System

  • 摘要: 研究非完整系统广义 Chaplygin方程的 Noether对称性与守恒量. 首先建立 Alem bert- L agrange原理的广义 Chaplygin形式. 其次给出时间和广义坐标的无限小变换, 研究这个原理在无限小变换下的变形形式, 得到系统的广义 Noether等式以及相应的守恒量, 并举例说明结果的应用.

     

    Abstract: The Noether symmetry and conserved quantity of generalized Chaplygin equations of nonholonomic system is studied. Firstly, a generalized Chaplygin form of d’ Alembert Lagrange principle is established. Secondly, the infinitesimal transformations of time and generalized coordinates are given and an invariance of the principle under the infinitesimal trarsformations is studied. Thirdly, the generalized Noether identity and corresponding conserved quantity are obtained. An example is finally given to illustrate the application of the result.

     

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