One of the earliest formulations of dynamics of nonholonomic systems traces back to 1895 and is due to Chaplygin, who developed his analysis under the assumption that a certain number of the generalized coordinates do not occur either in the kinematic constraints or in the Lagrange function. A few years later Voronec derived equations of motion for nonholonomic systems removing the restrictions demanded by the Chaplygin systems. Although the methods encountered in the following years favor the use of the quasi-coordinates, we will pursue the Voronec method, which deals with the generalized coordinates directly. The aim is to establish a procedure for extending the equations of motion to nonlinear nonholonomic systems, even in the rheonomic case.

非完整系统动力学的最早公式之一可以追溯到1895年，归功于Chaplygin，他在假设一定数量的广义坐标既不存在运动学约束也不存在Lagrange函数的情况下发展了他的分析。几年后，沃罗涅克导出了非完整系统的运动方程，从而消除了Chaplygin系统所要求的限制。尽管在接下来的几年中遇到的方法倾向于使用准坐标，但是我们将继续采用Voronec方法，该方法直接处理广义坐标。目的是建立一种即使在流变学情况下也能将运动方程扩展到非线性非完整系统的程序。