时间尺度上相空间中二阶线性可控力学系统的Noether理论

研究时间尺度上相空间中二阶线性可控力学系统的Noether对称性与守恒量.建立了时间尺度上二阶线性可控力学系统的Hamiton方程,给出该系统的Noether广义准对称性的定义和判据,并得到广义准对称性相应的Noether守恒量,文末举例说明其结果的应用.

非保守线性陀螺系统的稳定性

本文研究具有势力,陀螺力、循环力和瑞利阻尼的非保守线性力学系统的稳定性。借助于瑞利商证明了三个稳定性定理,这些定理给出的稳定性判据不依赖于瑞利商,因此方便实用。

Poincaré-Четаев变量下非线性非完整转动相对论系统的运动方程

研究Poincar啨-Четаев变量下非线性非完整转动相对论动力学系统的运动方程 .首先 ,引入Poincar啨 -Четаев变量x1,x2 ,… ,xn 及n -m个完整约束和m -l个Четаев型非完整约束 .其次 ,定义转动相对论系统的动能及加速度动能 ,然后由D′Alembert -Lagrange原理导出Chaplygin型方程、Nielsen型方程和Appell型方程 .

基于数字滤波器卷积核模型的系统响应误差分析与响应谱优化

响应谱被广泛应用于振动试验谱推导和振动台闭环控制,其计算精度取决于所采用的数字滤波器方法。首先构建了基于数字滤波器的线性力学系统强迫响应计算模型,然后提出了基于数字滤波器卷积核模型的系统响应误差分析方法,在此基础上对比了脉冲响应不变法、阶跃响应不变法、中心阶跃响应不变法、斜阶跃响应不变法及三点拉格朗日法引入的响应偏置误差和相位误差,最后基于三点拉格朗日数字滤波器对疲劳损伤谱和极值响应谱进行了优化分析。分析结果表明,在给定采样率下,三点拉格朗日法引入的偏置误差最小,且相位误差接近零。该方法可进一步提高响应谱计算精度,对利用响应谱推导振动试验谱和振动台闭环控制有实用价值。

广义线性非完整力学系统的Hojman守恒量

研究广义线性非完整力学系统的Lie对称性导致的Hojman守恒量,在时间不变的特殊Lie对称变换下,给出系统的Lie对称性确定方程、约束限制方程和附加限制方程,得到相应完整系统的Hojman守恒量以及广义线性非完整力学系统的弱Hojman守恒量和强Hojman守恒量,并举一算例说明结果的应用.

水轮机离心调速系统的混沌实验装置设计

水轮机是利用水流能量的重要动力机械,离心调速器是其重要组成部分。水轮机离心调速系统是一个非线性动力学混沌系统,在对离心调速系统进行动力学分析后,通过自制机械飞摆,使用无触点角度传感器和上位机,研究了离心调速系统混沌的物理量,直观地展示了混沌现象。该装置具有易组装、易调节、稳定性强等特点,为实际水轮机调速器的改进提供了理论与模型基础,同时能引导大学生关注生产实际,从中发现问题并提出自己的解决方法。

Pendulation reduction on ship-mounted container crane via T-S fuzzy model

Ship-mounted container cranes are challenging industrial applications of nonlinear pendulum-like systems with oscillating disturbance which can cause them unstable.Since wave-induced ship motion causes the hoisted container to swing during the transfer operation,the swing motion may be dangerously large and the operation must be stopped.In order to reduce payload pendulation of ship-mounted crane,nonlinear dynamics of ship-mounted crane is derived and a control method using T-S fuzzy model is proposed.Simulation results are given to illustrate the validity of the proposed design method and pendulation of ship-mounted crane is reduced significantly.

Symmetry Reduction of Two-Dimensional Damped Kuramoto-Sivashinsky Equation

In this paper, the problem of determining the largest possible set of symmetries for an important nonlinear dynamical system： the two-dimensional damped Kuramoto-Sivashinsky （（21）） DKS ） equation is studied. By applying the basic Lie symmetry method for the （217）） DKS equation, the classical Lie point symmetry operators are obtained. Also, the optimal system of one-dimensional subalgebras of the equation is constructed. The Lie invariants as well as similarity reduced equations corresponding to infinitesimal symmetries are obtained. The nonclassicaJ symmetries of the （2D） DKS equation are also investigated.

Nonlinear dynamics of flexible rotor system supported on fixed-tilting pad combination journal bearing

Based on the Reynolds equation with Reynolds boundary conditions, the Castelli method was employed to solve the Reynolds equation for oil lubrication upon bearings. By doing so, a profile of nonlinear oil film force of single-pad journal bearings is established. According to the structure of combination journal bearings, nonlinear oil film force of combination journal bearing is obtained by retrieval, interpolation and assembly techniques. As for symmetrical flexible Jeffcott rotor systems supported by combination journal bearings, the nonlinear motions of the center of the rotor are calculated by the self-adaptive Runge-Kutta method and Poincar6 mapping with different rotational speeds. The numerical results show that the system performance is slightly better when the pivot ratio changes from 0.5 to 0.6, and reveals nonlinear phenomena of periodic, period-doubing, quasi-periodic motion, etc.

Nonlinear dynamics analysis of a new autonomous chaotic system

In this paper,a new nonlinear autonomous system introduced by Chlouverakis and Sprott is studied further,to present very rich and complex nonlinear dynamical behaviors. Some basic dynamical properties are studied either analytically or nu-merically,such as Poincaré map,Lyapunov exponents and Lyapunov dimension. Based on this flow,a new almost-Hamilton chaotic system with very high Lyapunov dimensions is constructed and investigated. Two new nonlinear autonomous systems can be changed into one another by adding or omitting some constant coefficients.

The application of modeling and prediction with MRA wavelet network

As there are lots of non-linear systems in the real engineering, it is very important to do more researches on the modeling and prediction of non-linear systems. Based on the multi-resolution analysis (MRA) of wavelet theory, this paper combined the wavelet theory with neural network and established a MRA wavelet network with the scaling function and wavelet function as its neurons. From the analysis in the frequency domain, the results indicated that MRA wavelet network was better than other wavelet networks in the ability of approaching to the signals. An essential research was can:led out on modeling and prediction with MRA wavelet network in the non-linear system. Using the lengthwise sway data received from the experiment of ship model, a model of offline prediction was established and was applied to the short-time prediction of ship motion. The simulation results indicated that the forecasting model improved the prediction precision effectively, lengthened the forecasting time and had a better prediction results than that of AR linear model. The research indicates that it is feasible to use the MRA wavelet network in the short-time prediction of ship motion.

Nonlinear dynamics and coupling effect of libration and vibration of tethered space robot in deorbiting process

In order to control the growth of space debris,a novel tethered space robot(TSR) was put forward.After capture,the platform,tether,and target constituted a tethered combination system.General nonlinear dynamics of the tethered combination system in the post-capture phase was established with the consideration of the attitudes of two spacecrafts and the quadratic nonlinear elasticity of the tether.The motion law of the tethered combination in the deorbiting process with different disturbances was simulated and discussed on the premise that the platform was only controlled by a constant thrust force.It is known that the four motion freedoms of the tethered combination are coupled with each other in the deorbiting process from the simulation results.A noticeable phenomenon is that the tether longitudinal vibration does not decay to vanish even under the large tether damping with initial attitude disturbances due to the coupling effect.The approximate analytical solutions of the dynamics for a simplified model are obtained through the perturbation method.The condition of the inter resonance phenomenon is the frequency ratio λ_1=2.The case study shows good accordance between the analytical solutions and numerical results,indicating the effectiveness and correctness of approximate analytical solutions.

Improved control of intelligent excavator using proportional-integral-plus gain scheduling

Consider the design and implementation of an electro-hydraulic control system for a robotic excavator, namely the Lancaster University computerized and intelligent excavator (LUCIE). The excavator was developed to autonomously dig trenches without human intervention. One stumbling block is the achievement of adequate, accurate, quick and smooth movement under automatic control, which is difficult for traditional control algorithm, e.g. PI/PID. A gain scheduling design, based on the true digital proportional-integral-plus (PIP) control methodology, was utilized to regulate the nonlinear joint dynamics. Simulation and initial field tests both demonstrated the feasibility and robustness of proposed technique to the uncertainties of parameters, time delay and load disturbances, with the excavator arm directed along specified trajectories in a smooth, fast and accurate manner. The tracking error magnitudes for oblique straight line and horizontal straight line are less than 20 mm and 50 mm, respectively, while the velocity reaches 9 m/min.

Comparing dynamical systems concepts and techniques for biomechanical analysis

Traditional biomechanical analyses of human movement are generally derived from linear mathematics.While these methods can be useful in many situations,they do not describe behaviors in human systems that are predominately nonlinear.For this reason,nonlinear analysis methods based on a dynamical systems approach have become more prevalent in recent literature.These analysis techniques have provided new insights into how systems(1) maintain pattern stability,(2) transition into new states,and(3) are governed by short-and long-term(fractal) correlational processes at different spatio-temporal scales.These different aspects of system dynamics are typically investigated using concepts related to variability,stability,complexity,and adaptability.The purpose of this paper is to compare and contrast these different concepts and demonstrate that,although related,these terms represent fundamentally different aspects of system dynamics.In particular,we argue that variability should not uniformly be equated with stability or complexity of movement.In addition,current dynamic stability measures based on nonlinear analysis methods(such as the finite maximal Lyapunov exponent) can reveal local instabilities in movement dynamics,but the degree to which these local instabilities relate to global postural and gait stability and the ability to resist external perturbations remains to be explored.Finally,systematic studies are needed to relate observed reductions in complexity with aging and disease to the adaptive capabilities of the movement system and how complexity changes as a function of different task constraints.

Control of a Rigid-Flexible Satellite Solar Panel with Non-collocated Sensor/Actuator

This paper presents a model and analysis for a flexible link with non-collocations of sensors and actuators. It shows the changes in the system dynamics and the appearance of zeroes in the right-plan complex, turning the system a non-minimum phase system. The performance of the PID （proportional-integral-derivative） and LQR （linear quadratic regulator） controller are discussed considering the zero dynamics of the system in three points of special interest： （I） the collocated case, when the sensor is in the base of the link; （2） the critical case, where the system starts to present zeroes in the right-plan complex and （3） the limit case, when the sensors are in the end point of the flexible link. Investigation for a simple rigid-flexible model with one mode, in the three cases, the PID and LQR controller performance are damage. To deal with this kind of problem, new control techniques should be developed.

Abnormality diagnosis of cracks in the concrete dam based on dynamical structure mutation

A method of the fuzzy cross-correlation factor exponent in dynamics is researched and proposed to diagnose abnormality of cracks in the concrete dam. Moreover, the Logistic time series changing from period-doubling bifurcation to chaos is tested first using this method. Results indicate that it can distinguish inherent dynamics of time series and can detect mutations. Considering that cracks in the concrete dam constitute an open, dissipative and complex nonlinear dynamical system, a typical crack on the downstream face of a concrete gravity arch dam is analyzed with the proposed method. Two distinct mutations are discovered to indicate that the abnormality diagnosis of cracks in the concrete dam is achieved dynamically through this method. Furthermore, because it can be directly utilized in the measured crack opening displacement series to complete abnormality diagnosis, it has a good prospect for practical applications.

A simple algorithm for testing the stability of periodic solutions of some nonlinear oscillators with large time delay

Periodic solutions occur commonly in linear or nonlinear dynamical systems. In some cases, the stability of a periodic solution holds if the rightmost characteristic root has negative real part. Based on the Lambert W function, this paper presents a simple algorithm for locating the rightmost characteristic root of periodic solutions of some nonlinear oscillators with large time delay. As application, the proposed algorithm is used to study the primary resonance and 1/3 subharmonic resonance of the Duffing oscillator under harmonic excitation and delayed feedback, as well as the control problem of the van der Pol oscillator under harmonic excitation by using delayed feedback, with a number of case studies. The main advantage of this algorithm is that though very simple in implementation, it works effectively with high accuracy even if the delay is large.

OVERVIEW OF COMPLEX SYSTEMS IN SPORT

The complex systems approach offers an opportunity to replace the extant pre-dominant mechanistic view on sport-related phenomena.The emphasis on the environment-system relationship,the applications of complexity principles,and the use of nonlinear dynamics mathematical tools propose a deep change in sport science.Coordination dynamics,ecological dynamics,and network approaches have been successfully applied to the study of different sport-related behaviors,from movement patterns that emerge at different scales constrained by specific sport contexts to game dynamics.Sport benefit from the use of such approaches in the understanding of technical,tactical,or physical conditioning aspects which change their meaning and dilute their frontiers.The creation of new learning and training strategies for teams and individual athletes is a main practical consequence.Some challenges for the future are investigating the influence of key control parameters in the nonlinear behavior of athlete-environment systems and the possible relatedness of the dynamics and constraints acting at different spatio-temporal scales in team sports.Modelling sport-related phenomena can make useful contributions to a better understanding of complex systems and vice-versa.

SOME REMARKS ON THE NULL CONDITION FOR NONLINEAR ELASTODYNAMIC SYSTEM

The author derives the same null condition as in [1] for the nonlinear elastodynamic system in a simpler way and proves the equivalence of the null conditions introduced in [1] and [7] respectively.

Adaptive Event-Based Consensus of Multi-Agent Systems with General Linear Dynamics

In this paper, adaptive event-based consensus of multi-agent systems with general linear dynamics is considered. A novel adaptive event-based controller and a state-dependent triggering function are proposed for each agent. The consensus can be achieved without the assumption that（A, B） is stabilizable. Furthermore, the Zeno-behavior of the concerned closed-loop system is also excluded under certain conditions. Finally, a numerical simulation example is presented to show the effectiveness of the theoretical results.