Abstract: The objective is to study impact on non-holonomic systems with nonideal holonomic constraints. Considering first-order linear non-holonomic systems with redundant generalized coordinates, the Lagrange equations with unknown Lagrange multipliers are obtained. Based on the above equations, the relation between the states for pre-impact and post-impact is established. An example shows the procedure to realize the method.

Key words: nonideal constraint, first-order linear, non-hololonomic system, impact

摘要： 研究了当非完整系统中含有非理想的完整约束时的打击问题的拉格朗日方法。针对一阶线性非完整系统, 得到了含有多余广义坐标的非完整系统带乘子的拉格朗日方程, 在此基础上推导了系统受到打击时, 打击前后系统状态之间的关系及打击期间的约束反力冲量。在算例中, 详细描述了当打击冲量未知时该方法的实现过程。

关键词: 非理想约束, 一阶线性, 非完整系统, 打击