有阻尼单摆的冲击波解

研究和分析有阻尼单摆的运动方程,应用近似法方程时发现存在冲击波解并精确求解.同时结合有阻尼单摆的相图分析冲击波解存在的物理意义.     

弱阻尼非线性单摆的周期研究

用平均法研究了弱阻尼条件下非线性单摆的振动,得到周期比随角振幅和阻尼常量变化的表达式.     

Symmetry and chaos in the motion of the damped driven pendulum

The damped, driven pendulum equation is studied numerically. A relation is pointed out between the symmetry of the initial period-m dynamical state of am×2ⁿ period-doubling sequence and the form of the chaotic attractor for the final chaotic dynamical state reached after completion of the inverse-doubling sequence. Effects of extrinsic noise are also mentioned.     

Stability of the parametrically excited damped inverted pendulum: theory and experiment

The parametrically driven, damped, inverted pendulum can be dynamically stabilized in particular regions of the parameter space. The impact of damping on dynamic stabilization can be stabilizing or destabilizing depending on the location in parameter space (i.e., drive frequency and amplitude). Floquet analysis and numerical simulations were used to determine the stable regions. An experiment was conducted that verifies the model. Physical explanations and simple bounding approximations are provided to summarize findings. The utility of the highly damped pendulum results are illustrated by drawing the analogy to dynamic stabilization of the Rayleigh-Taylor instability: it permits ready demonstration that dynamic stabilization is impossible in that system absent surface tension.     

Optimal analytical and numerical approximations to the (un)forced (un)damped parametric pendulum oscillator

The (un)forced (un)damped parametric pendulum oscillator (PPO) is analyzed analytically and numerically using some simple, effective, and more accurate techniques. In the first technique, the ansatz method is employed for analyzing the unforced damped PPO and for deriving some optimal and accurate analytical approximations in the form of angular Mathieu functions. In the second approach, some approximations to (un)forced damped PPO are obtained in the form of trigonometric functions using the ansatz method. In the third approach, He's frequency-amplitude principle is applied for deriving some approximations to the (un)damped PPO. In the forth approach, He's homotopy technique is employed for analyzing the forced (un)damped PPO numerically. In the fifth approach, the p-solution Method, which is constructed based on Krylov–Bogoliúbov Mitropolsky method, is introduced for deriving an approximation to the forced damped PPO. In the final approach, the hybrid Padé-finite difference method is carried out for analyzing the damped PPO numerically. All proposed techniques are compared to the fourth-order Runge–Kutta (RK4) numerical solution. Moreover, the global maximum residual distance error is estimated for checking the accuracy of the obtained approximations. The proposed methodologies and approximations can help many researchers in studying and investigating several nonlinear phenomena related to the oscillations that can arise in various branches of science, e.g. waves and oscillations in plasma physics.     

Analysis of a damped pneumatic spring

The complex dynamic stiffness of a damped spring is determined. The damping is produced by transient pressure feedback from an auxiliary tank connected by a capillary to the spring cylinder. From the complex stiffness, the damping and stiffness are determined as functions of excitation frequency. The behavior of a compound spring, consisting of a damped pneumatic spring in parallel with a stiffer linear spring, is also examined. The analysis shows that the damping loss factor depends only on the tank/cylinder volume ratio, and that the capillary dimensions affect only the frequency at which maximum damping occurs. The compound spring is shown to have a maximum loss factor which quickly reaches an asymptotic value as the tank/cylinder volume ratio increases. From this presentation a clearer understanding of the behavior of a damped air spring, and a better sense of how design parameters affect the component's characteristics are obtained.     

利用智能手机磁传感器研究单摆运动

本文基于Phyphox手机App,利用智能手机中的磁传感器(电子罗盘)研究磁性单摆运动.结果表明,不同最大摆角测量出来的磁感应强度随时间变化规律不同.只有最大摆角小于1°时,单摆才可看作简谐振动.不同最大摆角的磁感应强度随时间变化曲线可以用磁偶极子模型结合大角度单摆公式来描述.利用磁传感器测量的当地重力加速度为9.868m/s²,由于磁性摆空气阻尼较小,测得的实验误差仅为0.8%.     

Analysis of the response of damped cylindrical shells carrying discontinuously constrained beam elements

A simple analysis is presented of the forced vibratory response of a cylindrical shell having a number of axial beams adhered to it by a viscoelastic material layer. The attached beams are identical, closely spaced and distributed around the full circumference of the shell. The excitation is a concentrated vibratory force acting radially at the mid-section on the surface of the shell. The end conditions of the shell and the attached beams are all assumed to be simply supported. The effects of the operational temperature and frequency on the viscoelastic material properties are considered. An experiment was conducted, for comparison, on a damped cylindrical shell suspended in air by lightweight elastic shock cords and driven at the mid-section by an electromechanical vibration shaker. Good correlations between the test data and analytical solutions were obtained over a wide range of frequencies.     

Coupled modes of the torsion pendulum

The coupling of the swing modes of a torsion pendulum to the torsional mode has been solved analytically. Our solution provides a clear explanation of why a magnetic damper is effective in suppressing unwanted modes in most gravitational experiments. The analytic solution also shows that the amplitude of the mode coupling is greatest at the lowest frequencies. This explains why mode coupling at the lowest frequency is all that is observed in the experiments reported here.     

单摆的振动图像演示装置

用电火花计时器作单摆的高压电源,使单摆的针尖和铜片间产生火花放电,并且在单放机带动而做匀速直线运动的纸带上产生放电点迹,形成单摆的振动图像.根据振动图像探究单摆的振动周期与振幅、摆长和摆的质量是否有关.     

Recoiling momentum of the electromagnetic-impulse pendulum

Summary This paper is intended to elucidate various disputed points discussed in a latter by P. N. Graneau relative to our criticism with respect to his work on the analysis of the electromagnetic-impulse pendulum. The main point of this note is to emphasize that the recoiling momentum of the projectile, in the electromagnetic-impulse pendulum, goes to the fixed frame and not to the radiated field.     

The damped self-interaction

A self-interaction with damped off-diagonal coefficients is used to illustrate techniques for dealing directly with Hamiltonians in strange representations of the CCR.     

Quantum theory of the damped harmonic oscillator

A phenomenological stochastic modelling of the process of thermal and quantal fluctuations of a damped harmonic oscillator is presented. The divergence of the momentum dispersion associated with the Markovian limit is removed by a Drude regularization. The variances of position and momentum are evaluated in closed form at arbitrary temperature and for arbitrary damping. Properties of real and imaginary time correlation functions are discussed, and a spectral decomposition of the equilibrium density matrix is given.     

Quantum decoherence of the damped harmonic oscillator

In the framework of the Lindblad theory for open quantum systems, we determine the degree of quantum decoherence of a harmonic oscillator interacting with a thermal bath. It is found that the system manifests a quantum decoherence which is more and more significant in time. We also calculate the decoherence time and show that it has the same scale as the time after which thermal fluctuations become comparable with quantum fluctuations. The text was submitted by the author in English.     

Canonical quantization of the Bateman-Morse-Feshbach damped oscillator

The Bateman-Morse-Feshbach classical formulation of the damped oscillator is canonically quantized. The spectrum of the Hamiltonian is given. It is shown that the wavefunctions behave asymptotically as a superposition of damped oscillators when their initial values belong to an appropriately-selected dense subset of the Hilbert space.partially supported by U.S. Army Grant DAAL03-87-K-0110.Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy.     

Torsion pendulum revisited

We present an analysis of the motion of a simple torsion pendulum and we describe how, with straightforward extensions to the usual basic dynamical model, we succeed in explaining some unexpected features we found in our data, like the modulation of the torsion mode at a higher frequency and the frequency splitting of the swinging motion. Comparison with observed values yields estimates for the misalignment angles and other parameters of the model.