Abstract
The form invariance and Lie symmetry of a variable mass nonholonomic mechanical system is studied. The definition and the criterion and the conserved quantity of form invariance and Lie symmetry for the variable mass nonholonomic mechanical system are given. The relation between the form invariance and Lie symmetry is obtained. An example is given to illustrate the application of the results.
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Noether A E. Invariant variantions problem[J].Nachr Akad Wiss Göttingen Math Phys, 1918, (2):235–257.
Lutzky M. Dynamical symmetries and conserved quantities[J].J Phys A, 1979,12(7):973–981.
Liu Duan. Noether’s theorem and its inverse theorem of nonholonomic nonconservative dynamical systems[J].Science in China Series A, 1990,20(11):1189–1197. (in Chinese)
Li Ziping.Classical and Quantum Constrained System and Their Symmetrical Properties[M]. Beijing University of Industry Press, Beijing, 1993. (in Chinese)
Zhao Yaoyu, Mei Fengxiang. On symmetry and invariant of dynamical system[J].Advances in Mechanics, 1993,23(3):360–372. (in Chinese)
Mei Fengxiang. Noether theorem of Birkhoff system[J].Science in China Series A, 1993,23(7): 709–717. (in Chinese)
Zhao Yaoyu. Conservative quantities and Lie’s symmetries of nonconservative dynamical systems [J].Acta Mechanica Sinica, 1994,26(3):380–384. (in Chinese)
Mei Fengxiang, Wu Runheng, Zhang Yongfa. Lie symmetries and conserved quantities of nonholonomic systems of non-Chetaev’s type[J].Acta Mechanica Sinica, 1998,30(4):468–474. (in Chinese)
Mei Fengxiang. Lie symmetries and conserved quantities of holonomic variable mass systems[J].Applied Mathematics and Mechanics (English Edition), 1999,20(6):629–634.
Mei Fengxiang.Applications of Lie Groups and Lie Algebras to Constrained Mechanical Systems [M]. Science Press, Beijing, 1999. (in Chinese)
Fang Jianhui. The conservation law of second-order nonholonomic system of non-Chetaev’s type [J].Applied Mathematics and Mechanics (English Edition), 2000,21(7):836–840.
Fang Jianhui. The conservation law of nonholonomic system of second-order non-Chetave’s type in event space[J].Applied Mathematics and Mechanics (English Edition), 2001,23(1):89–94.
Mei Fengxiang. Form invariance of Appell equations[J].Chinese Physics, 2001,10(3):177–180.
Wang Shuyong, Mei Fengxiang. On the form invariance of Nielsen equations[J].Chinese Physics, 2001,10(5):373–375.
Chen Xiangwei, Luo Shaokai, Mei Fengxiang. A form invariance of constrained Birkhoff system [J].Applied Mathematics and Mechanics (English Edition), 2002,23(1):53–57.
Wang Shuyong, Mei Fengxiang. Form invariance and Lie symmetry of equations of non-holonomic systems[J].Chinese Physics, 2002,11(1):5–8.
Fang Jianhui, Xue Qingzhong, Zhao Songqing. Form invariance of Nielsen equations of a noncon-servative mechanical system[J].Acta Physica Sinica, 2002,51(10):2183–2185. (in Chinese)
Li Renjie, Qiao Yongfen, Meng Jun. Form invariance of Gibbs-Appell equations for variable mass holonomic systems[J].Acta Physica Sinica, 2002,51(1):1–5. (in Chinese)
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Communicated by MA Xing-rui
Biography: FANG Jian-hui, Professor, E-mail: fangjh@hdpu.edu.cn
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Jian-hui, F., Pei-sheng, C. & Jun, Z. Form invariance and Lie symmetry of variable mass nonholonomic mechanical system. Appl Math Mech 26, 204–209 (2005). https://doi.org/10.1007/BF02438243
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DOI: https://doi.org/10.1007/BF02438243