周期运动

我们考虑B-做周期运动，即在S~2上会形成一个闭合曲线。

We just think about periodic motion of B | - , i.e. its trajectory form a closed curve in S ~ 2 .

多自由度含间隙振动系统周期运动的二重Hopf分岔

Double Hopf bifurcation of periodic motion of the multi-degree-of-freedom vibratory system with a clearance

存在间隙的多自由度系统的周期运动及Robust稳定性

Periodic motions and robust stability of the multi-degree-of-freedom systems with clearances

关于几乎周期运动f（p，t）的充要条件及其推论

On sufficient and necessary conditions of almost periodic recurrent motions f ( p , t ) and its corollary

计算结果表明，系统存在Hopf分叉及低周期运动。

The result of calculation shows that may undergo the Hopf bifurcation and quasi-periodic motions .

时滞位移反馈下Duffing系统的周期运动及其稳定性数值分析

Numerical Analysis of Periodic Motions and Their Stability of a Duffing Oscillator with a Delayed Displacement Feedback

认为电磁轴承系统由PD控制器产生的变刚度是一个能控制系统从混沌运动到周期运动的控制力。

Numerical approach through a computer software Dynamics is utilized to explore the existence of the periodic and chaotic motions in the rotor-AMB system with the time-varying stiffness .

由此直接得到Floquet指标和赝周期运动的边界。

From explicit solution follow directly Floquet exponent and the boundary of pseudo-periodic motion .

对于两个具有VanderPolDuffing型耦合的非线性振子，二次分叉一般会导致稳定的拟周期运动。

Generally , a stable quasiperiodic motion can be caused by the secondary bifurcation in two coupled Van der Pol-Duffing nonlinear oscillators .

此时隧穿表现出振幅衰减的准周期运动，同时会出现所谓的ESD现象。

We show that the tunneling exhibits the property of quasiperiodic with damping amplitude , at the same time the so-called ESD appears .

在该方法中，微扰控制变量、延迟时间τ、反馈权重因子k、加入延迟反馈控制信号的时间的选取，是把冗余度机器人的混沌运动转变成规则的周期运动的关键因素。

The disturbance variable , the delayed time " ", the feedback weight factor " k " and the time of adding delayed control signal are some key parameters for good chaotic control in the method .

针对地球质心运动主要是由多种周期运动叠加的特点，依次讨论了谱分析方法中的AR模型谱分析和小波谱分析方法。

In allusion to the characteristic that Geocentric Motion is piled up by several periodic motions , the spectral analysis by wavelet and AR were discussed in turn in this paper .

在一定的参数条件下，系统除了存在稳定的周期运动形态之外，还存在着倍周期分叉、Hopf分叉以及其他分叉，系统会沿着倍周期分叉、Hopf分叉等多种途径进入混沌运动。

With changes of parameters , besides stable periodic motion the system will lead to chaotic motion by ways of period doubling bifurcation and Hopf bifurcation .

按照增量式PID控制算法并利用可视化编程工具VC++6.0对转台控制程序进行了编制，分别给出了定点运动和周期运动的完整控制程序；

According to the incremental mode PID control algorithm , the control program for platform is compiled with the help of VC + + 6.0 . A complete control program for Fixed-point movement and Cycle movement is given respectively ;

研究表明：系统存在二次Hopf分岔，并导致准周期运动；存在重复的倍周期分岔，导致次谐运动；

It is found that the secondary Hopf bifurcation , a series of period-doubling bifurcation and the saddle-node bifurcation result in quasi-periodic motion , subharmonic adoption motion and jump phenomenon respectively .

对刚性约束的非线性动力系统进行研究，得到了该动力系统周期运动稳定性分析的Floquet特征乘子计算的半解析法。

A semi-analytic calculation method of Floquet multipliers is presented for the stability analysis of periodic motions in nonlinear dynamic systems with rigid constraints .

为了研究倍化分岔与Hopf分岔之间的联系，研究了一类碰撞振动系统因周期运动失稳而产生倍化分岔的问题。

In order to study the relation of the period-doubling bifurcation and the Hopf bifurcation , the period-doubling bifurcation problems of a vibro-impact system is investigated when the periodical solutions lose its stability .

在带模拟开关的RLC电路模型中发现V型阵发成为主要的从周期运动向混沌运动过渡的形式，这种阵发类型只能在分段光滑耗散系统中发生。

It is discovered in the RLC circuit model that type V intermittency becomes the main route of the transition from periodic motion to chaos . This type of intermittency can happen only in piecewise-smooth dissipative systems .

着重研究了一类存在间隙的双质体振动系统的周期运动在非共振和弱共振条件下的Hopf分叉。

A vibratory system with double masses and a gap is considered . Dynamics of the system are studied with special attention to Hopf bifurcations of period motions in non-resonance and weak resonance cases .

丢番图逼近、环面T~2上的Gevrey亚椭圆性与几乎周期运动

Diophantine Approximation , Gevrey Hypoellipticity and Almost Periodic Motion on the Torus T ~ 2

采用Floquet理论对转子-轴承系统周期运动的稳定性进行了分析，并给出了某些转速下的轴心轨迹和Poincar啨映射图。

Floquet theory was chosen for analysis of the stability of the periodic motions . Some journal center locus and Poincar é maps at different speeds were given .

应用Ott，Grebogi和Yorke的参数微调方法，使系统的运动状态由混沌变成所希望的周期运动。

The chaotic dynamic states of system are forced to the desired periodic motion states by the small adjusting parameter method of OGY .

给出一种在时域中模拟刚性剖面作周期运动辐射生成Stokes波的方法，为数值波浪水池试验提供高品质入射波模型。

To provide good quality incident waves in numerical wave tanks , a method was presented for simulation of Stokes wave generation in the time domain by a two dimensional rigid body periodically oscillating on a free water surface .

设计RBF神经网络非线性补偿控制器，提出了混沌系统线性状态反馈的复合控制方法，将可调系统混沌行为镇定到期望目标位置或者变成周期运动。

A nonlinear compensation controller with RBF neural networks was developed , a hybrid control technique for chaotic system based on linear state feedback was presented . The chaotic behavior of controlled system could be directed to the desired targets or periodic trajectory .

利用打靶法结合Floquet理论，对裂纹转子系统稳态周期运动的稳定性进行了分析与研究，揭示了裂纹转子系统同步周期运动分岔导致概周期运动与混沌运动的演变过程。

The nonlinear stability of the periodic motion of the rotor system with crack is investigated . Floquet theory and the shooting method is chosen to obtain the bifurcation patterns and the stability of periodic motions .

通过建立碰撞振动系统的物理模型和数学模型，利用正则模态矩阵法对碰撞振动系统进行解耦，并用解析法求解了碰撞振动系统周期运动的解析解和线性化矩阵和各个系统的Poincare映射。

By establishing physical model and mathematical model of the vibro-impact system , using regular modal matrix method to decouple the vibro-impact system , and working out the analytical solution , linear matrix and poincare mapping of different system by analytic method . 2 .

解析确定了该类含间隙系统周期运动的Poincar啨映射，研究了周期运动的稳定性，确定了周期运动的Hopf分叉值与横截条件。

The Poincar é map of the vibratory system with a gap is established . The stability of a class of periodic motions with one impact is investigated by analytical methods . Hopf bifurcation values and intersecting conditions of the period motions with one impact are determined .

有碰撞存在的多体振动系统的周期运动和稳定条件

Periodic Motion and Stability Condition of Multimass System Vibrating with Impact

引导混沌运动到周期运动的自适应控制策略

An adaptive control strategy for directing chaotic motion to periodic motion

三自由度双侧刚性约束振动系统的概周期运动

Quasi-periodic motions of a three-degree-of-freedom vibrating system with two rigid constrains