Stable Periodic Motion of a System Using Echo for Position Control

We study a system of equations which is based on Newton's law and models automatic position control by echo. Rewritten as a delay differential equation with state-dependent delay the model defines a semiflow on a submanifold in the space of continuously differentiable maps [-h, 0] ². All time-t maps and the restriction of the semiflow given by t > h are continuously differentiable. For simple nonlinearities and suitable parameters we find a set of initial data to which the solution curves return, after an excursion into the ambient manifold. The associated return map is semiconjugate to an interval map. Estimates of derivatives yield a unique, attracting fixed point of the latter, which can be lifted to the return map. The proof that the resulting periodic orbit is stable and exponentially attracting with asymptotic phase involves a Poincaré return map and a discussion of derivatives of its iterates.     

RESEARCH OF THE PERIODIC SOLUTION FOR A CLASS OF NONLINEAR DIFFERENTIAL EQUATIONS

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非自治系统用瞬态响应求周期解稳定度的方法

根据Floquet理论关于线性周期系数系统解的性质及稳定性条件,定义了衡量非线性非自治系统周期解受扰后的衰减速率指标-稳定度.从动力系统流的概念出发,给出了利用非线性非自治系统稳态周期解受扰后的瞬态响应信息计算周期解稳定度的方法.以不平衡滑动轴承-弹性转子系统为例,说明了该方法的有效性.将稳定度等于零作为临界判据,该方法不仅解决了工频周期解失稳边界的确定问题,而且解决了渐进稳定域的估计和抗冲击扰动裕度的计算问题.     

一类多自由度非线性动力系统周期解的定性分析

应用摄动法的思想和子空间映射的技巧，给出一类多自由度非线性动力系统周期解的存在性、唯一性和稳定性的判别法。该法把问题归结为初等积分的计算。其主要特点是计算简单，应用方便。文后给出了两个例子。     

一类线性Liénard方程周期边值问题解的存在唯一性的构造性证明

利用初值问题方法给出了一类线性Liénard方程周期边值问题解的存在唯一性的构造性证明,利用数值延拓方法,并给出了计算实例和一种大范围求解这类方程周期解的方法。