Abstract: The time-integral theorems for nonholonom ic mechanical systems in velocity space were studied.Firstly,considering the force ,which was the function of the radius vector and velocity r·- and time t,the c oncept of acc eleraton energy in velocity space was introduced.Secondly,from the Newtion s dy namical equation for system of particles,the Routh s form equations for nonholon omic mechanical systems in velocity space were derived and the generalized viria l theorem was obtained.On the basis of the theore...