Kovalevskaya弹性杆  

ELASTIC ROD IN KOVALEVSKAYA CASE

作　　者：刘延柱[1] 

机构地区：[1]上海交通大学工程力学系,上海200030

出　　处：《力学与实践》2003年第5期21-23,共3页Mechanics in Engineering

摘　　要：应用Kirchhoff比拟讨论Kovalevskaya情况弹性细杆的平衡稳定性问题.导出Kirchhoff方程的解析积分.对于杆截面的主轴与Frenet坐标轴重合的无扭转杆的特殊情形作定性分析,讨论其平衡状态的稳定性与分岔.证明了判断受拉扭作用的圆截面直杆平衡稳定性的Greenhill公式也适用于Kovalevskaya情形的非圆截面杆.Using the Kirchhoff analogy, the stability and tifurcation of a thin elastic rod in Kovalevskaya case is discussed in this paper. The analytical integrals of Kirchhoff equations are derived, and a qualitative analysis is conducted for the special case of a twistless rod when the principal axes of the cross section is coincident with the Frenet axes. It is shown that the Greenhill criterion for the straight rod with a circular cross section under the action of tension and torsion is also valid for the rod with a noncircular cross section in Kovalevskaya case.

关 键 词：Kovalevskaya弹性细杆 Kirchhoff比拟 平衡稳定性 刚体动力学 分岔 拉扭作用 KIRCHHOFF方程 

分 类 号：O313.3[理学—一般力学与力学基础]