中文摘要：

包括受到单方的锁或开的限制的一根自我旋转的伸臂横梁的一个简单 non-holonomic 系统的一个非线性的动态模型被采用一般哈密尔顿的变化原则建立。临界数值，小平衡在失去它的稳定性或单方的限制被激活或僵绳节点分叉发生，并且 equilibria 被近似分析、数字的方法调查。结果显示弄弯的 equilibria 和横梁的分叉模式是不同的取决于单方的限制的清理的距离是否等于零并且单方的限制是否被锁。单向性的猛咬彻底地现象(即大祸现象) 被注定发生在系统不管限制是否是锁能。僵绳节点分叉能仅仅在单方的限制是能的锁，它的清理是非零的条件上发生。二个方法获得的结果是一致的。

英文摘要：

A nonlinear dynamic model of a simple nonholonomic system comprising a self-rotating cantilever beam subjected to a unilateral locked or unlocked constraint is established by employing the general Hamilton＇s Variational Principle. The critical values, at which the trivial equilibrium loses its stability or the unilateral constraint is activated or a saddle-node bifurcation occurs, and the equilibria are investigated by approximately analytical and numerical methods. The results indicate that both the buckled equilibria and the bifurcation mode of the beam are different depending on whether the distance of the clearance of unilateral constraint equals zero or not and whether the unilateral constraint is locked or not. The unidirectional snap-through phenomenon （i.e. catastrophe phenomenon） is destined to occur in the system no matter whether the constraint is lockable or not. The saddle-node bifurcation can occur only on the condition that the unilateral constraint is lockable and its clearance is nonzero. The results obtained by two methods are consistent.