The Routh equation of a nonholonomic system with a nonlinear constraint equation that is expandable to MacLaurin progression on generalized velocity, can be obtained by Lagrangian multiplier method and d'Alembert principle in an ideal constraint condition. Chetaev condition is valid in linear nonholonomic system only, and is eguivalent to Vacco condition. The so-called “Euler condition" can unite Chetaev condition and Vacco condition, can unite d'Alembert principle and Hamilton principle, and can resolve all existing problems in nonlinear nonholonomic system.