FANG Jian-hui. Lie Symmetries and Conserved Quantities of Second-Order Nonholonomic Mechanical System[J]. Applied Mathematics and Mechanics, 2002, 23(9): 982-986.
 Citation: FANG Jian-hui. Lie Symmetries and Conserved Quantities of Second-Order Nonholonomic Mechanical System[J]. Applied Mathematics and Mechanics, 2002, 23(9): 982-986.

# Lie Symmetries and Conserved Quantities of Second-Order Nonholonomic Mechanical System

• Rev Recd Date: 2002-01-31
• Publish Date: 2002-09-15
• The Lie symmetries and the conserved quantities of the second-order nonholonomic mechanical system are studied. Firstly, by using the invariance of the differential equation of motion under the infinitesimal transformations, the determining equations and the restriction equations of the Lie symmetries of the system are established, and the structure equation and the conservative quantities of the Lie symmetries are obtained. Secondly, the inverse problems of the Lie symmetries are studied. Finally, an example is given to illustrate the application of the result.
•  [1] 刘端.非完整非保守力学系统的Noether定理及其逆定理[J].中国科学,A辑,1990,20(11):1189-1197. [2] LIU Duan.Noether's theorem and its inverse of nonholonomic nonconservative dynamical systems[J].Science in China,Series A,1990,34(2):419-429. [3] 赵跃宇,梅凤翔.关于力学系统的对称性与守恒量[J].力学进展,1993,23(3):360-372. [4] Lutzky M.Dynamical symmetries and conserved quantities[J].J Phy A,Math Gen,1979,12(7):973-981. [5] 赵跃宇.非保守力学系统的Lie对称和守恒量[J].力学学报,1994,26(3):380-384. [6] WU Run-heng,MEI Feng-xiang.On the Lie symmetries of the nonholonomic mechanical systems[J].J of BIT,1997,6(3):229-235. [7] 梅凤翔,吴润衡,张永发.非Четаев型非完整系统的Lie对称性与守恒量[J].力学学报,1998,30(4):468-474. [8] 梅凤翔.变质量完整力学系统的Lie对称与守恒量[J].应用数学和力学,1999,20(6):592-596. [9] 刘荣万,傅景礼.非完整非保守力学系统在相空间的Lie对称性与守恒量.应用数学和力学,1999,20(6):597-601. [10] 梅凤翔.利用Jourdain原理研究二阶非完整系统的守恒律[J].北京理工大学学报,1998,18(1):17-21. [11] 方建会.二阶非Четаев型非完整系统的守恒律[J].应用数学和力学,2000,21(7):755-758. [12] 梅凤翔.非完整动力学研究[M].北京:北京工业学院出版社,1987,50-51.

### Catalog

###### 通讯作者: 陈斌, bchen63@163.com
• 1.

沈阳化工大学材料科学与工程学院 沈阳 110142