In their well-known work A new perspective on constrained motion F.E.Udwadia and R.E.Kalaba have derived equations of motion for nonholonomic systems that didnt include constraint reaction forces. The number of these equations is equal to the number of generalized coordinates of a system. Udwadia and Kalaba suppose that the equations obtained by them are the simplest and moreover most comprehensive so far discovered. These equations are derived with the help of the E.Moore inverse, which was proposed in 1920 and generalized in 1955 by R.Penrose. The equations are written in a compact matrix form, but nevertheless it is difficult to use them in practice because of the poorly known Moore-Penrose inverse. In the paper offered a tensor form of the Udwadia-Kalaba equations of motion for nonholonomic systems is given, which is simple and illustrative. It is derived as a result of substitution of expressions for generalized reaction forces, which are given by the second group of the Maggi equations, into the Lagrange equations of the second kind with multipliers.