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1.
由于不同的非惯性系具有不同的加速度,导致单摆在不同的非惯性系中具有不同的振动周期,所以有必要掌握非惯性系下单摆振动周期的计算.基本的计算方法是利用非惯性系动力学方程,结合受力分析求解,但这种方法既要考虑惯性力,又需要进行力的分解,比较麻烦.本文通过引入惯性力势能,给出非惯性系机械能守恒定律,并利用机械能守恒定律对处于特定非惯性系中的单摆周期进行分析计算,得出非惯性系中单摆的振动周期不仅与单摆自身属性有关,而且与非惯性系的运动加速度或角速度有关的结论. 相似文献
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本文在实验教学中引入一种非线性混沌摆系统,通过调节混沌摆的驱动力周期演示了该非线性动力学系统出现混沌现象的过程,从而让学生了解混沌现象的参数敏感性、相图特点、频谱特性等基本特性.为了进一步了解该混沌摆的特性,本文建立了该非线性摆系统的简化动力学方程,在数值上对其进行了研究.基于动力学方程的数值模拟,克服了实验上相关参数定量改变困难、摆动稳定性不易控制、实验时间周期长等问题.在数值模拟中,通过改变不同参数得到了相图、频谱图以及分岔图,比较深入详细地对这种混沌摆的相关特性进行了描述,也有利于学生加深对混沌摆的理解. 相似文献
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Aline Souza de Paula Francisco Heitor Iunes Pereira-Pinto 《Journal of sound and vibration》2006,294(3):585-595
Pendulum is a mechanical device that instigates either technological or scientific studies, being associated with the measure of time, stabilization devices as well as ballistic applications. Nonlinear characteristic of the pendulum attracts a lot of attention being used to describe different phenomena related to oscillations, bifurcation and chaos. The main purpose of this contribution is the analysis of chaos in an experimental nonlinear pendulum. The pendulum consists of a disc with a lumped mass that is connected to a rotary motion sensor. This assembly is driven by a string-spring device that is attached to an electric motor and also provides torsional stiffness to the system. A magnetic device provides an adjustable dissipation of energy. This experimental apparatus is modeled and numerical simulations are carried out. Free and forced vibrations are analyzed showing that numerical results are in close agreement with those obtained from experimental data. This analysis shows that the experimental pendulum has a rich response, presenting periodic response, chaos and transient chaos. 相似文献
4.
A ferrofluid torsion pendulum in an oscillating magnetic field exhibits a rich variety of nonlinear self-oscillatory regimes. The dynamics is governed by the system of coupled differential equations for the in- and off-axis components of the fluid magnetization and the pendulum angular deflection. In the limiting case of high driving frequency, the system reduces to the sole Rayleigh-type equation. Much more complicated temporal patterns arise when the field frequency and the pendulum eigen frequency are of the same order. 相似文献
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We analyse the use of parametric and quasiperiodic modulations in suppressing horseshoe structure in the phase plane of perturbed
pendulum systems. Taking the Froude pendulum as a typical system, four different modulation mechanisms are studied by deriving
analytic expressions for the window of the strength of modulation giving suppression in each case. A comparison of the four
cases from the point of view of flexibility and efficiency is also given. 相似文献
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The vibration response of a spring-mass-damper system with a parametrically excited pendulum hinged to the mass is investigated using the harmonic balance method. The approximate results are found to be fairly consistent with those obtained by the numerical calculation. The vibrating regions of the pendulum system are obtained which are similar to those given by Mathieu's equation. Based on the analysis of three parameters in the response equation, the characteristics of response of the system are clarified. The stabilities of the harmonic solutions are analyzed, and finally our proposed approximation is verified compared with the numerical results. 相似文献
8.
对受迫非线性单摆系统进入混沌的道路进行了研究,发现单摆系统的运动是极其复杂的.目前在其他系统发现的进入混沌的通道,在该系统中几乎均可找到.这是一个介绍混沌运动的典型系统. 相似文献
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L. A. Savrov 《Il Nuovo Cimento C》1989,12(5):681-683
Summary The possibility to detect Allais effect by the paraconic pendulum with the needle and ball suspension is considered. Foucalt
force and friction force are estimated with the conclusion to use the ball suspension system for pendulum. 相似文献
11.
Holger R. Dullin 《Zeitschrift für Physik B Condensed Matter》1994,93(4):521-528
Melnikov's method is applied to the planar double pendulum proving it to be a chaotic system. The parameter space of the double pendulum is discussed, and the integrable cases are identified. In the neighborhood of the integrable case of two uncoupled pendulums Melnikov's integral is evaluated using residue calculus. In the two limiting cases of one pendulum becoming a rotator or an oscillator, the parameter dependence of chaos, i.e. the width of the separatrix layer is analytically discussed. The results are compared with numerically computed Poincaré surfaces of section, and good agreement is found. 相似文献
12.
This paper presents a numerical study of an autoparametric system composed of two elements: a pendulum and an excited nonlinear oscillator. Owing to an inertial coupling between the two elements, different types of motion are possible, from periodic to chaotic. This study examines a linear induction of an energy harvester depending on the pendulum motion. The harvester consists of a cylindrical permanent magnet mounted on a rotor and of four windings fixed to the housing as a stator. When the pendulum is rotating or swinging, the converter is generating energy due to magnetic induction. In this paper, a method utilizing parametrical resonance for harvesting energy from low frequency vibrations is studied. The authors compare energy induced by different types of pendulum motion: swinging, rotation and chaotic dynamics. Additionally, voltage values for different parameters of excitation are estimated. 相似文献
13.
Dynamical systems with nonlinear damping show interesting behavior in the periodic and chaotic phases. The Froude pendulum
with cubical and linear damping is a paradigm for such a system. In this work the driven Froude pendulum is studied by the
harmonic balancing method; the resulting nonlinear response curves are studied further for resonance and stability of symmetric
oscillations with relatively low damping. The stability analysis is carried out by transforming the system of equations to
the linear Mathieu equation. 相似文献
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Complex responses are studied for a spherical pendulum whose support is excited with a translational periodic motion. Governing equations are studied analytically to allow prediction of responses under various excitation conditions. Stability for certain cases of damping is predicted by means of existing analysis and compared with experimental data. Numerical time-step integration of the governing equations is developed to predict responses for various types of excitation and damping conditions. Predicted results are compared with corresponding motions measured in an experimental spherical pendulum system. A data acquisition system is included whereby detailed digitized time histories of the pendulum motion can be established and various parameters can be computed to characterize the type of motion present. Two new vector spaces are defined for describing complex responses which occur for certain specified excitation conditions. It is shown in these parameter spaces that the transition from quasiperiodic to chaotic motions can be carefully quantified in systems with very light damping. This discovery provides a convenient means for comparison of complex motions in the numerical and experimental air pendulum systems. The implications of the results are important for dynamic response in various applications, including fluid motions in satellite tanks and other nonlinear time-dependent physical processes which include very light damping. (c) 1995 American Institute of Physics. 相似文献
17.
利用基于SOS的SPG200高压脉冲功率装置研究了有机玻璃(PMMA)和尼龙1010在变压器油中的闪络特性。研究结果表明:闪络电压随内电极直径增加近似指数增加,随闪络距离延长近似线性增加,相应的击穿时延也近似线性增加。受实验条件的影响,有机玻璃和尼龙1010的闪络性能略有差异。同轴径向电场降落集中在内电极表面附近一定径向距离内,同轴电场下的闪络电压主要由内电极表面电场与径向电场分布的均匀程度决定。增加内电极直径和延长闪络距离都可以提高闪络电压,而增加内电极直径的效果更显著。 相似文献
18.
Miroslav Pardy 《International Journal of Theoretical Physics》2007,46(4):848-859
The Lagrange theory of particle motion in the noninertial systems is applied to the Foucault pendulum, isosceles triangle
pendulum and the general triangle pendulum swinging on the rotating Earth. As an analogue, planet orbiting in the rotating
galaxy is considered as the giant galactic gyroscope. The Lorentz equation and the Bargmann-Michel-Telegdi equations are generalized
for the rotation system. The knowledge of these equations is inevitable for the construction of LHC where each orbital proton
“feels” the Coriolis force caused by the rotation of the Earth. 相似文献
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针对基础水平运动的弹簧摆的非线性动力学响应进行研究,利用拉格朗日方程建立了系统的动力学方程.将离散傅里叶变换、谐波平衡法以及同伦延拓方法相结合,对系统的周期响应进行求解,避免了传统方法计算中使用泰勒展开引起的小振幅的限制,与数值计算结果的对比表明该求解方法具有较高的精确度.利用Floquet理论分析了周期响应的稳定性,给出了基础运动振幅和频率对系统周期响应的影响.研究发现:对应某些基础频率和振幅,系统的周期响应可能发生Hopf分岔;利用数值计算研究了Hopf分岔后系统响应随基础频率和振幅的变化,发现系统出现了倍周期运动、拟周期运动和混沌等复杂的动力学行为.研究表明系统进入混沌的主要路径是拟周期环面破裂和阵发性. 相似文献