Abstract
Lindelöf' s equation is derived by using the Vakonomic model, which shows that Lindelöf' s work coincides with Vakonomic model. Chaplygin' s equation is derived by using Chetaev' s model, which shows that Chaplygin' s work coincides with Chetaev' s model. On basis of these, by improving the expressions of Chaplygin' s equation and Lindelöf' s equation, the reasonable transition from Chaplygin' s equation to Lindelöf's equation is realized, the reasonable transition from Lindelöf's equation to Chaplygin' s equation is realized too. Finally, a typical example is given. The work of this paper shows that, just as the Vakonomic model and Chetaev's model are complementary to each other, Lindelöf' s work and Chaplygin' s work are complementary to each other too.
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References
Chaplygin S A.The Research of Non- Holonomic System Dynamics [M]. Moskwa: The State Technical Press, 1949. (in Russian)
Voronets A S. On motion equation of non-holonomic systems [J].Math Handbook, 1901,22(4): 659 ∼ 680. (in Russian)
Novoselov V S. Generalized motion equation of non-linear non-holonomic systems [J].Mechanics, Journal of LGU, 1957,21(7):53 ∼ 62. (in Russian)
MEI Feng-xiang.The Mechanical Foundation of Non-Holonomic System [M]. Bei**g: Bei**g Industry Istitute Press, 1985. (in Chinese)
CHEN Bin. The holonomity and non-holonomity of non-linear constraint in non-holonomic system [J].Science in China, 1993,23(8):836 ∼ 846. (in Chinese)
LIANG Li-fu, SHI Zhi-fei. Variational problem of general displacement in non-Holonomic system [J].Acta Mechanica Solida Sinica, 1993,6(4):357 ∼ 364.
GUO Zhong-heng. Reasonable solution of kind of non-holonomic mechanical problem [J].Science in China, 1994,24(5):485 ∼ 497. (in Chinese)
MEI Feng-xiang. The free motion of non-Holonomic system and disappearance of the non-holonomic property [J].Acta Mechanica Sinica, 1994,26(4):470 ∼ 476. (in Chinese)
Pars L A.An Introduction to the Calculus of Variations [M]. London: Heinemann, 1962.
Rosonberg R M.Analytical Dynamics of Discrete Systems [M]. New York: Pleum Press, 1977.
Greenwood D T.Classical Dynamics [M]. Englewood Cliffs, N J: Prentice-Hall, Inc, 07632, 1997.
HUANG Shao-du, JI Hui-yu.Analytical Mechanics [M]. Bei**g: Tsinghua University Press, 1985. (in Chinese)
CHEN Bin. Analytical Dynamics [M]. Bei**g: Peking University Press, 1987. (in Chinese)
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Communicated by CHENG Chang-jun
CLC number: 0316
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Li-fu, L., Wei-dong, C. The complementary property of Lindelöf's work and Chaplygin's work. Appl Math Mech 21, 937–946 (2000). https://doi.org/10.1007/BF02428364
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DOI: https://doi.org/10.1007/BF02428364