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 Jamalc)
a Department of Modern Physics, University of Science and Technology of China, P. O. Box 4, Hefei 230026, China; b Institut 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
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.
Received: 25 September 2008
Revised: 25 November 2008
Accepted manuscript online:
Fund: 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.
Cite this article:
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 2009 Chin. Phys. B 18 3131
Altmetric calculates a score based on the online attention an article receives. Each coloured thread in the circle represents a different type of online attention. The number in the centre is the Altmetric score. Social media and mainstream news media are the main sources that calculate the score. Reference managers such as Mendeley are also tracked but do not contribute to the score. Older articles often score higher because they have had more time to get noticed. To account for this, Altmetric has included the context data for other articles of a similar age.
