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

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.