庞加莱映射

第四，建立了刚性磁浮轴承转子系统空间状态方程，用数值积分法和庞加莱映射方法对其稳定性进行了研究。

Fourthly , the space state equation of the rigidity magnetic rotor-bearing system is set up , and a study has been conducted on the stability of magnetic rotor-bearing system with the use of numerical integration and Poincare map method .

定性的研究工作有：研究系统运动的相轨图、庞加莱映射图、功率谱图和自相关函数图；

The qualitative work including : research the phase trajectory of the system 、 Poincare map 、 power spectral and auto-correlation .

由于带膝关节的被动行走机器人在一个行走步态周期内包含两个摆动阶段和两个碰撞切换过程，因此庞加莱映射的建立和Floquet乘子的计算成为分析机器人局部稳定性的关键。

Since one walking cycle of the passive walking robot with knees is separated into two swing phases and two impact phases , the construction of poincar é mapping and the calculation of floquet multiplier are critical to analyze the local stability of biped robot .

第二部分提供了混沌吸引子精细化观察、分析和应用的新工具。应用小波分析方法、庞加莱映射和功率谱分析技术，分析研究推进电机系统的混沌吸引子特征；

In the second part , chaos attractor characteristics have been analyzed by wavelet analysis , power spectra and analysis poincare map .

基于由飞行器、行星及其卫星组成圆型限制性三体问题模型，通过庞加莱映射的方法，研究了飞行器从行星卫星附近逃逸的问题。

Escaping trajectories are investigated using a Poincar é map method in the circular restricted three body problem consisting of spacecraft , planet and moon .

利用庞加莱映射将周期轨道的稳定性分析转化为映射平面上不动点的稳定性分析。

With the help of Poincare mapping , the stability problem of periodic orbits was changed to that of the fixed points on the mapping plane .

通过数值仿真得到转子在此种状态下工作转速时的幅频图、时域图以及庞加莱映射图等。

Through the numerical simulation , several diagrams of rotor under the running condition were obtained , such as spectrum graph , Poincare graph and so on .

通过数值模拟，模拟了该系统的时间演化图、相图、分岔图、庞加莱映射图以及最大李雅普诺夫指数谱图，并进行了分析。

Time evolution , phase diagrams , bifurcation diagram , Poincare map , and largest Lyapunov in-dex spectrogram of the system are plotted by means of numerical simulations .

通过一系列的庞加莱映射将8维连续空间转化为7维的离散空间，进而通过牛顿-拉夫森算法进行迭代求解出相应庞加莱截面上的不动点。

Through a series of Poincare maps 8-dimensional continuous space can be reduced into discrete 7-dimensional space , then the fixed point on the corresponding Poincare section is solved by Newton-Raphson algorithm .

因此我们利用相应的分段线性系统的几何特征，通过求解庞加莱映射的不动点来研究周期解的存在性，并给出了例子用以检验结论的正确性。

With the help of geometrical observations for a corresponding piece-wise linear system , we derive an analytical method to investigate the existence of periodic orbits that are obtained by searching for the fixed points of Poincare maps .

最后以行波运动为例进行了实验仿真。再次，论文利用庞加莱映射对蛇形机器人的平面运动进行了稳定性分析。

At last we set traveling wave locomotion as an example to do the experiment and simulation . Thirdly , we made the stability analysis of snake-like robot locomotion on the planar surface based on Poincare ' maps .

利用被动跳跃步态周期性特点，合理降维定义了四足机器人被动跳跃步态的庞加莱映射，运用牛顿迭代法获得了庞加莱映射的某个固定点。

The Poincar é map of the quadruped bound gait is defined with reasonable dimensional reduction according to the characteristics of the periodic cycle . A fix point of Poincar é map is figured out with Newton-Raphson method .

利用分岔图分析稳定性与参数的关系，并且画出了倍周期分岔图的相图和庞加莱映射，使倍周期通向混沌过程表现得更明显直观。

By plotting bifurcation diagrams , the relation between stability versus parameters of the impact system is analyzed . And the phase plane portrait and Poincar é map of structure exhibit the process of the system motion from double-period to chaos more obviously .

第三章计算了强电场中锂原子的电离率，通过庞加莱映射找到了位形空间电离谱和相空间同宿缠绕的对应。

In the third chapter , we calculate autoionization rate of Rydberg lithium atoms in a static electric field . Through the Poincar é map found a direct connection between the ionization spectrum in general geometric space and the homoclinic tangle manifolds in phase space is found .

全局稳定性的大小由吸引域大小来评定，本文采用庞加莱胞映射方法计算了吸引域的大小。

The global stability is defined as the size of the basin of attraction , which is calculated by the Poincar é cell mapping method .

为解决流体混沌混合的可视化问题，本文提出采用逆向庞加莱胞映射方法，来控制混沌系统数值模拟过程中的初始误差敏感，用插值胞映射的方法，来提高模拟效率。

In order to solve the visualization problem of fluid chaotic mixing , in the paper a backward Poincare cell mapping ( BPCM ) method has been developed to control the evolution of error and the interpolation cell mapping method is used for the simulation efficiency .

对于这两类系统，利用一定的技巧，可以建立一个二维庞加莱（Poincare）映射。

For these two classes of equations , we can establish a two-dimensional Poincare map using some technique .