求解非线性动力系统周期解的改进打靶法

针对有周期解的动力系统边值问题可以转化为初值问题这一特点，改进了周期解的打靶 法数值求解. 在计算边界条件代数方程关于待定初值参数导数的过程中利用前一次 Runge-Kutta方法计算得到的节点函数值并通过再次利用Runge-Kutta方法获得了该导数值. 用此方法求解了Duffing方程及非线性转子---轴承系统的周期解,用Floquet理论判断了 周期解的稳定性,与普通打靶法作了比较,验证了方法的有效性.

AN IMPROVED METHOD FOR DETERMINING PERIODIC SOLUTIONS OF NOLINEAR DYNAMICAL SYSTEM

Boundary value problems for dynamical systems with periodic solutions can be turned into initial value problems.With this point in mind,the paper improves the shooting method.In the process of computing derivatives of boundary conditions' algebraic equations,which are functions of unknown initial value parameters, the node function values are obtained through Runge-Kutta method,and by using Runge-Kutta method once more,the derivatives can be obtained.The validity of such a method is verified by using it to obtain periodic solutions of Duffing equation and nolinear rotor-bear system,and comparing the results with those computed by traditional method.Meanwhile,we discuss the stability of the solutions by Floquet theory.