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 inco...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.展开更多
The purpose of this paper is to establish, paralleling a well-known result for definite integrals, the conditional convergence of a family of trigonometric sine series. The fundamental idea is to group appropriately t...The purpose of this paper is to establish, paralleling a well-known result for definite integrals, the conditional convergence of a family of trigonometric sine series. The fundamental idea is to group appropriately the terms of the series in order to show absolute divergence of the series, given the well-established result that the series as it stands is convergent.展开更多
基金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)Li Shu-Min is grateful to DAAD and DFG for financial supportduring his stay in Germany
文摘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.
文摘The purpose of this paper is to establish, paralleling a well-known result for definite integrals, the conditional convergence of a family of trigonometric sine series. The fundamental idea is to group appropriately the terms of the series in order to show absolute divergence of the series, given the well-established result that the series as it stands is convergent.
