中文摘要：

有在柱体的限制下面的圆形的生气的节的有弹性的杆的稳定性和颤动被讨论。抑制的杆的动力学的微分方程作为描述生气的节的态度的变量与 Euler 的角度被建立。在限制下面的螺旋状的平衡的存在条件作为杆的一种特殊配置被讨论。螺旋状的平衡的稳定性分别地在静电干扰和动力学的领域被讨论。为螺旋状的杆的稳定性的必要条件在空间领域和时间领域被导出，并且 Lyapunov 的家之间的差别和 Euler 是稳定性概念被讨论。有柱体限制的螺旋状的杆的曲折颤动的免费频率在分析形式被获得。

英文摘要：

The stability and vibration of an elastic rod with a circular cross section under the constraint of a cylinder is discussed. The differential equations of dynamics of the constrained rod are established with Euler＇s angles as variables describing the attitude of the cross section. The existence conditions of helical equilibrium under constraint are discussed as a special configuration of the rod. The stability of the helical equilibrium is discussed in the realms of statics and dynamics, respectively. Necessary conditions for the stability of helical rod are derived in space domain and time domain, and the difference and relationship between Lyapunov＇s and Euler＇s stability concepts are discussed. The free frequency of flexural vibration of the helical rod with cylinder constraint is obtained in analytical form.