梯度折射率介质下的光路计算与成像研究

使用激光照射具有梯度折射率的介质将形成海市蜃楼现象的光路轨迹"可视化"。主要研究了不同波长的激光在线性和非线性梯度折射率介质中的光路轨迹和成像情况。基于几何光学原理推导了光路方程并使用Matlab光线追迹算法计算了线性和非线性情况下的成像。实验上,通过自制仪器配置有折射率梯度的溶液并观察光路轨迹以及拍摄实物成像。实验拍摄的光路轨迹与理论推导基本一致,为海市蜃楼等现象的演示以及成像问题的研究提供了新的参考。     

检测前跟踪中的目标交叉航迹标签分层管理EI北大核心CSCD

针对检测前跟踪算法无法提供目标航迹标签以及传统算法在轨迹交叉情况下批次编号管理混乱的问题,提出了一种标记关联的航迹管理方法。该方法为各个目标的方位航迹标记不重复的标签,并针对标签多伯努利算法非共轭先验的问题,采用将标签多伯努利分布逼近δ-广义标签多伯努利分布的方法进行解决。另外还提出一种辅助门限进行分层逐级更新的方法,实现了对不同的航迹赋予不同的标签,解决了方位交叉情况下轨迹中断、目标跟丢和错跟的问题。仿真及海试试验表明,该方法的平均误差稳定且接近为0,定位精度高且轨迹连续清晰,不仅能在目标轨迹交叉时进行准确跟踪,还能实现对多目标数的精准估计,为基于声呐阵的水下目标态势感知方法提供了新的技术支持。     

电传飞行控制系统信号补偿技术

针对履带式移动机器人的轨迹跟踪控制问题进行研究,首先,建立了履带式移动机器人的运动学模型和跟踪误差模型;其次,设计了转速有限时间控制和线速度滑模控制的轨迹跟踪控制律,并给出了考虑运动受限作用下的控制律修正表达式;最后,基于MATLAB对所提控制律进行仿真,对比分析了不考虑运动受限情况下跟踪控制效果。结果表明,设计的跟踪控制律能够实现履带式移动机器人对圆轨迹的有效跟踪,且考虑运动受限作用的控制律更加符合实际。文章研究分析了运动受限作用对于移动机器人轨迹跟踪控制的影响,分析结果对其他移动机器人的运动控制研究具有参考价值。     

考虑运动受限的履带式移动机器人轨迹跟踪控制

针对履带式移动机器人的轨迹跟踪控制问题进行研究,首先,建立了履带式移动机器人的运动学模型和跟踪误差模型；其次,设计了转速有限时间控制和线速度滑模控制的轨迹跟踪控制律,并给出了考虑运动受限作用下的控制律修正表达式；最后,基于MATLAB对所提控制律进行仿真,对比分析了不考虑运动受限情况下跟踪控制效果;结果表明,设计的跟踪控制律能够实现履带式移动机器人对圆轨迹的有效跟踪,且考虑运动受限作用的控制律更加符合实际;文章研究分析了运动受限作用对于移动机器人轨迹跟踪控制的影响,分析结果对其他移动机器人的运动控制研究具有参考价值。     

切断库仑势的Regge极点

本文讨论了非相对论、切断库仑势的S矩阵元在复轨道角动量和复能量平面上的解析性质。在四种特殊情况下,求得了这S矩阵元的Regge极点。最后,在一般情况下,用数值计算了这S矩阵元的起始的两条Regge轨迹。     

一维间断流的数值计算

本工作不用伪粘性方法而将各种间断视为流动区域边界,从而数值地计算了平面、柱面及球面对称情况下均匀、静止、高压理想气体爆炸产物的绝热膨胀,给出了各间断轨迹和流场参数,并通过三种情况下算得结果的比较,考察了连续方程中几何聚散项的作用。     

上海光源储存环恒流注入束流安全性模拟

针对恒流注入过程中在同步辐射光闸开启情况下的辐射安全问题，对注入电子束轨迹进行了模拟跟踪计算，考察电子束在什么样的极端情况下会从光束线通道打出造成辐射安全事故。束流动力学模拟采用Accelerator Toolbox (AT)程序，正向跟踪电子轨迹。在不丢失任何可能性的前提下，放大入射电子束相空间，减小跟踪距离，简化计算。通过模拟结果得到机器安全联锁保护条件，为保障安全的恒流注入提供依据。     

三平动绳牵引并联机器人轨迹预处理算法

研究了一种新型飞行摄像平台,能够实现摄像机在大范围的三维空间内可以沿任意轨迹快速运动的摄像平台;摄像平台的运动由四台伺服电机带动四根缆绳并联拖动;绳牵引并联机器人是一种将电机的运动和力以绳为介质并行地转换为末端执行器运动和力的装置,具有结构简单、工作空间大、惯性小等优点;运动过程中满足轨迹光滑、不能出现停顿、振动,为了获得连续、平稳、无噪声的轨迹,文章采用轨迹预处理的方法,当出现轨迹不光滑,且影响了拍摄质量的情况下,采用三次样条圆弧插补的方法对其进行光滑处理,仿真结果表明该圆弧插补预处理算法能够很好地解决吊舱在高速运行而引起加速度过大的问题,进而达到提高运行效率的目的。     

基于Algodoo对不同情况的斜抛运动研究

基于斜抛运动规律,结合相应问题,利用Algodoo仿真实验平台深入研究在有和没有空气阻力情况下斜抛运动的轨迹、射程、射高、速度和加速度之间的差异,同时在考虑空气阻力的情况下对影响斜抛运动射程、射高的因素进行探究,并提出了将所得研究结果融入"斜抛运动"教学的相关建议.     

“甲虫爬环”问题的解析

比较简捷、直观地运用质点系动力学解析"甲虫爬环"问题,进一步解得甲虫以及原来与甲虫相接触的圆环上"标记点"的轨迹方程,并描绘出不同质量比情况下二者的轨迹,标记点的运动轨迹是圆内旋轮线.     

Entropy method of measuring and evaluating periodicity of quasi-periodic trajectories

This paper presents a method for measuring the periodicity of quasi-periodic trajectories by applying discrete Fourier transform (DFT) to the trajectories and analyzing the frequency domain within the concept of entropy. Having introduced the concept of entropy, analytical derivation and numerical results indicate that entropies increase as a logarithmic function of time. Periodic trajectories typically have higher entropies, and trajectories with higher entropies mean the periodicities of the motions are stronger. Theoretical differences between two trajectories expressed as summations of trigonometric functions are also derived analytically. Trajectories in the Henon-Heiles system and the circular restricted three-body problem (CRTBP) are analyzed with the indicator entropy and compared with orthogonal fast Lyapunov indicator (OFLI). The results show that entropy is a better tool for discriminating periodicity in quasiperiodic trajectories than OFLI and can detect periodicity while excluding the spirals that are judged as periodic cases by OFLI. Finally, trajectories in the vicinity of 243 Ida and 6489 Golevka are considered as examples, and the numerical results verify these conclusions. Some trajectories near asteroids look irregular, but their higher entropy values as analyzed by this method serve as evidence of frequency regularity in three directions. Moreover, these results indicate that applying DFT to the trajectories in the vicinity of irregular small bodies and calculating their entropy in the frequency domain provides a useful quantitative analysis method for evaluating orderliness in the periodicity of quasi-periodic trajectories within a given time interval.     

强激光场中CO分子经典轨迹的辛算法

采用辛算法计算CO异核双原子分子系统在强激光场作用下的经典轨迹,与Runge-Kutta方法进行比较,分析了CO双原子分子在激光场作用下的振动轨迹、相平面轨道与总能量随时间的变化及CO分子的解离.     

Coherent States and Modified de Broglie-Bohm Complex Quantum Trajectories

This paper examines the nature of classical correspondence in the case of coherent states at the level of quantum trajectories. We first show that for a harmonic oscillator, the coherent state complex quantum trajectories and the complex classical trajectories are identical to each other. This congruence in the complex plane, not restricted to high quantum numbers alone, illustrates that the harmonic oscillator in a coherent state executes classical motion. The quantum trajectories we consider are those conceived in a modified de Broglie-Bohm scheme. Though quantum trajectory representations are widely discussed in recent years, identical classical and quantum trajectories for coherent states are obtained only in the present approach. We may note that this result for standard harmonic oscillator coherent states is not totally unexpected because of their holomorphic nature. The study is extended to coherent states of a particle in an infinite potential well and that in a symmetric Poschl-Teller potential by solving for the trajectories numerically. For the Gazeau-Klauder coherent state of the infinite potential well, almost identical classical and quantum trajectories are obtained whereas for the Poschl-Teller potential, though classical trajectories are not regained, a periodic motion results as t→∞. Similar features were found for the SUSY quantum mechanics-based coherent states of the Poschl-Teller potential too, but this time the pattern of complex trajectories is quite different from that of the previous case. Thus we find that the method is a potential tool in analyzing the properties of generalized coherent states.     

Turbulent vortex wake: Classification principles,gauge equivalence,examples, and applications

The paper proposes a system of second-order ordinary differential equations with solutions interpreted as trajectories of a turbulent vortex wake. The trajectories are modeled by complexes of geodesic lines in non-Euclidean geometries and are analyzed to select a proper geometry by choosing a particular gauge for modeling the whole class of turbulent vortex wake trajectories. Examples are given of geodesic and partially geodesic gauges to model a particular complex of linear vortex wake trajectories, and possible ways are suggested to apply the theory to turbulence mesodynamics in cosmic plasma.     

Iterative solutions of the Lotka-Volterra equations

Summary Lotka-Volterra equations for two-species predator-prey system are solved by an iteration method. The first iteration step reproduces elliptical trajectories known from the linearization treatment. The second iteration step leads to analytical expressions describing large-amplitude motions and lying beyong the elliptical approximation. The range of validity of the method is discussed. It is shown that deviations from the exact trajectories increase if the initial state is far from the centre of motion. For illustration some trajectories are calculated showing a good agreement with trajectories obtained by numerical methods.     

Effects of self-fields on electron trajectory and gain in planar wiggler free-electron lasers with two-stream and ion-channel guiding

The effects of self-fields on electron trajectories and gain in planar wiggler free-electron lasers with two-stream and ion-channel guiding are investigated. An analysis of the two-stream quasi-steady-state electron trajectories is given by solving the equation of motion in the presence of ion-channel guiding and the planar wiggler. The electron trajectories and the gain are derived. The stability of the trajectories, the characteristics of the linear gain, and the normalized maximum gain are studied numerically. The numerical calculations show that there are eight group trajectories rather than the two groups reported in the absence of the self-fields. It is also shown that the normalized gain group seven （G7） decreases while the rest increases with the increase in normalized ion-channel frequency. The two-stream instability and the self-field lead to a decrease in the maximum gain, except for G7.     

Periodic orbits for classical particles having complex energy

This Letter revisits earlier work on complex classical mechanics in which it was argued that when the energy of a classical particle in an analytic potential is real, the particle trajectories are closed and periodic, but that when the energy is complex, the classical trajectories are open. Here it is shown that there is a discrete set of eigencurves in the complex-energy plane for which the particle trajectories are closed and periodic.     

Asymptotics of trajectories for cone potentials

We study the asymptotics of trajectories of the classical Hamiltonian dynamics. For Hamiltonians with cone potentials we have shown earlier that all trajectories are asymptotically free [5], i.e. the asymptotic velocities exist. Here we show that the generic trajectories are asymptotically uniform, i.e. the asymptotic phases exist.     

Statistical study of the trajectories of the air masses flow in the Alpine area

Summary As a part of our activity in the transboundary transport, this study examines a five years’ trajectory climatology interesting Northern Italy. Our analysis is twofold: firstly we examine the statistics of air masses arriving at an Alpine location (Brenner Pass) separating between rainy only trajectories and all trajectories, and, secondly, we study the climatology of trajectories, going out from the Po Valley. Trajectories are computed by means of a simple three-dimensional trajectory method using the wind data obtained by the analysis of the ECMWF. The distribution of the arrival (or departure) directions of the trajectories is presented and commented. The differences in the travel times for the different directions are presented as well. The vertical distribution of the trajectories is finally computed. The main results are discussed.