The Lie Symmetries and Conserved Quantities of Variable-Mass Nonholonomic System of Non-Chetaev's Type in Phase Space
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摘要: 在相空间引入无限小群变换,研究变质量非Четаев型非完整系统的Lie对称和守恒量.利用系统运动微分方程在无限小群变换下的不变性建立Lie对称的确定方程和限制方程,得到Lie对称的结构方程和守恒量,并举例说明结果的应用.Abstract: The Lie symmetries and the conserved quantities of a variable mass nonholonomic system of non-Chetaev's type are studied by introducing the infinitesimal transformations of groups in phase space. By using the invariance of the differential equations of motion under the infinitesmal transformations of groups,the determining equations and the restriction equations of the Lie symmetries of the system are established,and the structure equations and the conserved quantities are obtained. An example is given to illustrate the application of the result.
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Key words:
- nonholonomic system /
- phase space /
- analytic mechanics /
- variable mass /
- Lie symmetry /
- conserved quantity
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