钟摆模型极限环的存在性研究

钟摆系统是一类典型的分段光滑系统,结合Filippov系统刻画语言,解释了当钟摆无能量补充时,钟摆最终会停止在滑动集上的原因.利用数值模拟的方法,给出钟摆系统在有能量补充时,存在极限环的条件.最后,结合环域定理证明了一般的钟摆模型存在唯一稳定的极限环.     

高分辨率CMOS相机沿轨长条带钟摆式搜索成像设计

为实现面阵相机对沿轨方向长条带区域一定重叠率的推凝视成像,设计了高分辨CMOS传感器的钟摆式搜索成像模型.通过长条带逐层区域划分和成像重叠率渐近变化构建,计算了钟摆式搜索成像参量和卫星实时推凝指向姿态,并利用多次小幅逼近的PD控制器分析了搜索成像姿态控制精度与成像像移失配量.利用高分CMOS原理样机和小卫星姿控仿真平台对P5型曲面LED靶标系统进行地面等比缩放的长条带钟摆式搜索成像仿真试验.结果表明:帧间重叠率大于85%的钟摆式搜索成像比全凝视成像区域扩大了4倍;控制周期为10 Hz时,其姿态控制精度优于0.05°,姿态稳定度优于0.003°/s,搜索成像对应的图像传递函数能够达到0.141 1.     

An Abnormal Vibrational Mode of Torsion Pendulum

In the experiment for the determination of the gravitational constant G,we found an abnormal vibrational mode of the torsion pendulum.The abnormal mode disappeared as a magnetic damper was introduced to the torsion pendulum system.Our experimental results also show that the magnetic damper can be used to suppress the high frequency vibrational noises to torsion pendulums effectively.     

钟摆状态下湿颗粒坍塌流动行为及其动力相似性

基于建立的湿颗粒离散动力学模型,本文系统研究了钟摆状态下湿颗粒柱在重力驱动下的坍塌流动过程,主要考虑了颗粒粒径、液体表面张力系数和液体含量等参数对系统坍塌流动模式和动力学行为的影响。研究发现,在湿颗粒系统中,颗粒粒径和液体表面张力系数会改变颗粒间的毛细力大小,引起系统发生不同的坍塌流动模式,而液体含量仅定量影响颗粒坍塌后的堆积形态。在此基础上,进一步探讨了不同模式下系统坍塌流动行为与模型参数的相关性,发现无量纲Bond数是决定钟摆状态下湿颗粒物质坍塌流动动力学行为的本质因素。     

Pendulum with linear damping and variable length

The methods of multiple scales and approximate potential are used to study pendulums with linear damping and variable length. According to the order of the coefficient of friction compared with that of the slowly varying parameter of length, three different cases are discussed in details. Asymptotic analytical expressions of amplitude, frequency and solution are obtained. The method of approximate potential makes the results effective for large oscillations. A modified multiple scales method is used to get more accurate leading order approximations when the coefficient friction is not small. Comparisons are also made with numerical results to show the efficiency of the present method.     

Dynamical Behaviour of a Modulated Torsion Pendulum in Test of Weak Equivalence Principle

The dynamic behaviour of a modulated torsion pendulum used to test the weak equivalence principle (WEP) is studied in detail. Theoretical analysis shows that the pendulum will be driven by a force with double-frequency of the rotating turntable no matter whether the WEP is valid or not. This double-frequency effect should be considered for improving the sensitivity of the modulated pendulum in test of the WEP.     

Performance of an Accelerometer Suspended by a Pendulum

Performances of an accelerometer suspended by a pendulum and set on ground directly are both discussed. Theoretical analysis shows that the isolation from seismic disturbances of such a suspending accelerometer is equal to that of a narrow band-pass electronic filter. This means that the effect of seismic noises to the accelerometer can be substantially suppressed by means of a pendulum suspension during its performance tests.     

Stability Analysis of an Inverted Pendulum Subjected to Combined High Frequency Harmonics and Stochastic Excitations

Stability of vertical upright position of an inverted pendulum with its suspension point subjected to high frequency harmonics and stochastic excitations is investigated. Two classes of excitations, i.e., combined high frequency harmonic excitation and Gaussian white noise excitation, and high frequency bounded noise excitation, respectively, are considered. Firstly, the terms of high frequency harmonic excitations in the equation of motion of the system can be set equivalent to nonlinear stiffness terms by using the method of direct separation of motions. Then the stochastic averaging method of energy envelope is used to derive the averaged Ito stochastic differential equation for system energy. Finally, the stability with probability 1 of the system is studied by using the largest Lyapunov exponent obtained from the averaged Ito stochastic differential equation. The effects of system parameters on the stability of the system are discussed, and some examples are given to illustrate the efficiency of the proposed procedure.