Abstract: Making use of conclusions from [1]: (1) d-δ operations are commutative; (2) the Appell-Chetaev condition restricting virtual displacements is superfluous, the present paper derives the Lagrange equation without multipliers for a class of first-order nonlinear nonholonomic dynamical systems by means of variational principle. This kind of equations is new.

Key words: nonholonomic dynamics, d-δ commutativity, Appell-Chetaev condition