中文摘要：

在分析三类不等价的非完整变分，即vakonomic变分、Suslov变分和Holder变分的基础上，利用Lagrange乘子法和稳定作用量原理，讨论非线性非完整约束系统在这三类变分下的运动微分方程，论证了这三类微分方程等价的条件．作为一般约束系统的特例，得到了仿射非完整约束系统的运动微分方程．最后借助两个实例验证了结论的正确性．

英文摘要：

Based on an analysis of three kinds of non-equivalent nonholonomic variations, i.e., the Suslov＇s variation, Holder＇s variation and vakonomic variation, the method of Lagrange multipliers and stationary action principle are utilized to discuss the differential equations of motion for nonlinear nonholonomic constrained systems with respect to the three kinds of variations. The condition for the three kinds of equations to be equivalent is investigated. The equations for affine nonholonomic constrained systems are also obtained as special cases of the general nonholonomic systems. Two examples are given to illustrated the validity of the result.