A counterexample of the Euler condition: the Appell—Hamel dynamical system on a horizontally moving plate

doi:10.1088/1674-1056/18/8/005

中国物理B ›› 2009, Vol. 18 ›› Issue (8): 3131-3134.doi: 10.1088/1674-1056/18/8/005

A counterexample of the Euler condition: the Appell—Hamel dynamical system on a horizontally moving plate

徐山杉¹, 李书民², BerakdarJamal³

(1)Department of Modern Physics, University of Science and Technology of China, P. O. Box 4, Hefei 230026, China; (2)Department of Modern Physics, University of Science and Technology of China, P. O. Box 4, Hefei 230026, China \sjb)Institut f\"ur Theoretische Physik, Universit\"at Heidelberg, Philosophenweg 16, 69120 Heidelberg, Germany; (3)Insitut f\"ur Physik, Martin-Luther-Universit\"at Halle-Wittenberg, Heinrich-Damerow-St. 4, 06120 Halle, Germany

收稿日期:2008-09-25 修回日期:2008-11-25 出版日期:2009-08-20 发布日期:2009-08-20
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos 10874169 and 10674125), and the National Basic Research Program of China (Grant No 2007CB925200), and Li Shu-Min is grateful to DAAD and DFG for financial support during his stay in Germany.

A counterexample of the Euler condition: the Appell—Hamel dynamical system on a horizontally moving plate

Xu Shan-Shan(徐山杉)^a), Li Shu-Min(李书民)^a)b)^†, and Berakdar Jamal^c)

^a Department of Modern Physics, University of Science and Technology of China, P. O. Box 4, Hefei 230026, China; ^bInstitut für Theoretische Physik, Universit\"at Heidelberg, Philosophenweg 16, 69120 Heidelberg, Germany; ^c Insitut für Physik, Martin-Luther-Universit\"at Halle-Wittenberg, Heinrich-Damerow-St. 4, 06120 Halle, Germany

Received:2008-09-25 Revised:2008-11-25 Online:2009-08-20 Published:2009-08-20
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos 10874169 and 10674125), and the National Basic Research Program of China (Grant No 2007CB925200), and Li Shu-Min is grateful to DAAD and DFG for financial support during his stay in Germany.

摘要/Abstract

摘要： As a counterexample of the Euler condition for nonholonomic constraint problems [H. C. Shen, Acta Phys. Sin. 54, 2468 (2005)], we investigate the Apell--Hamel dynamical system on a horizontally moving plate. The inconsistency of the results with Newton mechanics suggests that the Euler condition is not a universal model for nonlinear nonholonomic systems. This is attributed to the fact that the virtual displacements so obtained are not normal to the constraint forces.

Abstract: As a counterexample of the Euler condition for nonholonomic constraint problems [H. C. Shen, Acta Phys. Sin. 54, 2468 (2005)], we investigate the Apell--Hamel dynamical system on a horizontally moving plate. The inconsistency of the results with Newton mechanics suggests that the Euler condition is not a universal model for nonlinear nonholonomic systems. This is attributed to the fact that the virtual displacements so obtained are not normal to the constraint forces.

Key words: Euler condition, nonholonomic constraint, Appell--Hamel dynamical system, Newton solution

中图分类号: (Lagrangian and Hamiltonian mechanics)

45.20.Jj

05.45.-a (Nonlinear dynamics and chaos)

徐山杉, 李书民, BerakdarJamal. A counterexample of the Euler condition: the Appell—Hamel dynamical system on a horizontally moving plate[J]. 中国物理B, 2009, 18(8): 3131-3134.

Xu Shan-Shan(徐山杉), Li Shu-Min(李书民), and Berakdar Jamal . A counterexample of the Euler condition: the Appell—Hamel dynamical system on a horizontally moving plate[J]. Chin. Phys. B, 2009, 18(8): 3131-3134.

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A counterexample of the Euler condition: the Appell—Hamel dynamical system on a horizontally moving plate

A counterexample of the Euler condition: the Appell—Hamel dynamical system on a horizontally moving plate

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