提高多体系统离散时间传递矩阵法计算精度的研究

深入探讨多体系统离散时间传递矩阵法对平面、空间刚体-光滑铰多体系统运动响应的研究。提出提高该方法计算精度和计算稳定性的方法，导出相应的多端刚体传递矩阵。设计了角坐标的迭代循环，该变量不必采用近似形式，因而提高了计算精度和计算稳定性。其它方法有：1)增加泰勒展开式的高阶项；2)合理选择将速度、加速度表示为位移的线性函数的方法(本文简称线性化方法)；3)合理确定迭代循环的初值等。对4种多体系统进行了计算机仿真研究，表明本文提出的方法有效。     

Nanometric positioning accuracy in the presence of presliding and sliding friction: Modelling,identification and compensation

Presliding and sliding frictional effects, limiting the performances of ultrahigh precision mechatronics devices, are studied in this work. The state-of-the-art related to frictional behavior in both motion regimes is, hence, considered, and the generalized Maxwell-slip (GMS) friction model is adopted to characterize frictional disturbances present in a micromanipulation device. All the parameters of the model are identified via experimental set-ups and included in the overall MATLAB/SIMULINK model. With the aim of compensating frictional effects, the modelled response of the system is thus compared to experimental results when using proportional-integral-derivative (PID) control, feed-forward model-based compensation and a self-tuning adaptive regulator. The adaptive regulator proves to be the most efficient and is, hence, used in the final repetitive point-to-point positioning tests allowing to achieve nanometric precision and accuracy.     

一类非二次微分食饵一捕食系统的定性分析

本文通过一系列变换，将一类非二次微分食饵—捕食系统化为二次微分系统Ⅲ类方程的标准形式，进而研究了该系统极限环的存在唯一性，并运用Liapunov第二方法论证了正平衡点的稳定性，进而又得出相应极限环的稳定性.     

Determination of limit cycles for a modified van der Pol oscillator

The determination of amplitude and period of limit cycles is a crucial question in non-linear mechanics. In this paper, a van der Pol oscillator containing a periodic potential is considered. Amplitude and period of limit cycles are calculated by He’s variational method and Krylov–Bogoliubov–Mitropolsky (KBM) method.     

陀螺仪漂移测试小角度伺服法实验方案的改进

为了提高陀螺仪的使用精度,研究了陀螺仪漂移测试的伺服法实验技术.依托973项目,在国内首次完成了高精度单自由度静压液浮陀螺仪的伺服法实验.找到了影响小角度伺服法实验测试精度的主要误差源,即小角度伺服法实验的方法误差,通过对该误差的分析,提出了改进的小角度伺服实验方案.建立了小角度伺服法实验方法误差的仿真模型,用改进方案和原始方案分别进行了仿真和实验,结果表明改进方案同原始方案相比,陀螺仪漂移误差模型中的三项系数辨识精度均有提高.     

Analytical study of a triple Hopf bifurcation in a tritrophic food chain model

We provide an analytical proof of the existence of a stable periodic orbit contained in the region of coexistence of the three species of a tritrophic chain. The method used consists in analyzing a triple Hopf bifurcation. For some values of the parameters three limit cycles born via this bifurcation. One is contained in the plane where the top-predator is absent. Another one is not contained in the domain of interest where all variables are positive. The third one is contained where the three species coexist. The techniques for proving these results have been introduced in previous articles by the second author and are based on the averaging theory of second-order. Existence of this triple Hopf bifurcation has been previously discovered numerically by Kooij et al.     

二维抛物型方程的一族高精度显式差分格式

构造了一族解二维抛物型方程的高精度显格式 ,其稳定性条件为r=Δt/Δx2 =Δt/Δy2 <1 /2 ,截断误差为O(Δt3 +Δx4)     

Ten limit cycles around a center-type singular point in a 3-d quadratic system with quadratic perturbation

In this paper, we show that perturbing a simple 3-d quadratic system with a center-type singular point can yield at least 10 small-amplitude limit cycles around a singular point. This result improves the 7 limit cycles obtained recently in a simple 3-d quadratic system around a Hopf singular point. Compared with Bautin’s result for quadratic planar vector fields, which can only have 3 small-amplitude limit cycles around an elementary center or focus, this result of 10 limit cycles is surprisingly high. The theory and methodology developed in this paper can be used to consider bifurcation of limit cycles in higher-dimensional systems.