Abstract: Analyzed the restricted condition with 1-order nonholonomic constraint, the form of 1-order nonholonomic ideal constraint force in the space of C^q is given, and the geometric significance in the velocity space is clarified. It＇s proved that Appell-Chetaev condition is sufficient and necessary condition to realizing 1-order nonholonomic ideal constraint.

Key words: l-order nonholonomic constraint, ideal constraint force, the velocity space, Lagrange＇s multiplier, virtual work, virtual displacement, Chetaev condition, virtual variation of generalized velocity