弹性细杆弯曲的Kirchhoff方程的违约校正求解

采用Euler四元数表示的Kirchhoff方程来研究受力挤压作用下的弹性细杆的拓扑构形，进一 步研究弹性细杆的力学性质；将得到的微分方程与约束条件组成微分代数方程后再转化为微 分方程规范形式以便求解；为满足边界条件，应用数值打靶法求解边值条件，并将弹性细杆 在力作用下的拉压过程用Matlab仿真出来.同时对由于误差导致的违约现象进行处理，并针 对欧拉参数的特征，选取合适的修正系数以保持方程的稳定性. 关键词： DNA Euler四元数 Kirchhoff方程 弹性细杆 违约修正

Solution of the Kirchhoff equation for thin elastic rod under bending by constraint violation correction method

To further study the mechanical property of a thin elastic rod, this paper will employ the Kichhoff equation which takes the form of Euler quaternion and study the topological configuration of the rod under compression. Adding the constraint condition to the differential equation, we can get a differential-algebraic equation(DAE).In order to be solved easily, DAE will be transformed into a c riterion form. To satisfy the boundary condition, we apply the shooting techniq ue to get the solution satisfying the boundary condition, and imitate the proced ure of pulling and pressing of thin elastic rod suffering a force. Simultaneousl y,to deal with the constraint stabilization phenomenon which is caused by errors , and according to the Euler quaternion character, we select a proper correction coefficient to keep the stability of the differential equation.