Kirchhoff方程的相对常值特解及其Lyapunov稳定性

Special solutions of Kirchhoff equations and their Lyapunov stability

对于超细长弹性杆静力学的Kirchhoff方程,用动力学的概念和方法研究其常值特解和稳定性问题.计算了 Kirchhoff方程相对固定坐标系、截面主轴坐标系以及中心线Frenet坐标系的常值特解,进行了Kirchhoff动力学比拟, 用一次近似理论分别讨论了它们的Lyapunov稳定性,导出了若干稳定性判据,并在参数平面上绘出了稳定域.

The special solutions of the Kirchhoff equations,which are those relative to fixed coordinate system,principal coordinate system of a cross section of the rod,and Frenet coordinate system of the central line of the rod,respectively,are derived in this paper. Lyapunov stability of these solutions is discussed by use of theory on the first-approximation stability,and at the same time stability area in parameter's plane is given.