Lie symmetry and Hojman conserved quantity of a Nielsen equation in a dynamical system of relative motion with Chetaev-type nonholonomic constraint

The Lie symmetry and Hojman conserved quantity of Nielsen equations in a dynamical system of relative motion with nonholonomic constraint of the Chetaev type are studied. The differential equations of motion of the Nielsen equation for the system, the definition and the criterion of Lie symmetry, and the expression of the Hojman conserved quantity deduced directly from the Lie symmetry for the system are obtained. An example is given to illustrate the application of the results.

KANE’S EQUATIONS FOR PERCUSSION MOTION OF VARIABLE MASS NONHOLONOMIC MECHANICAL SYSTEMS

In this paper,the Kane’s equations for the Routh’s form of variable massnonholonomic systems are established.and the Kane’s equations for percussion motionof variable mass holonomic and nonholonomic systems are deduced from them. Secondly,the equivalence to Lagrange’s equations for percussion motion and Kane’sequations is obtained,and the application of the new equation is illustrated by anexample.

Equation of Motion of a Mass Point in Gravitational Field and Classical Tests of Gauge Theory of Gravity

A systematic method is developed to studY the classical motion of a mass point in gravitational gauge field. First, by using Mathematica, a spherical symmetric solution of the field equation of gravitational gauge field is obtained, which is just the traditional Schwarzschild solution. Combining the principle of gauge covariance and Newton＇s second law of motion, the equation of motion of a mass point in gravitational field is deduced. Based on the spherical symmetric solution of the field equation and the equation of motion of a mass point in gravitational field, we can discuss classical tests of gauge theory of gravity, including the deflection of light by the sun, the precession of the perihelia of the orbits of the inner planets and the time delay of radar echoes passing the sun. It is found that the theoretical predictions of these classical tests given by gauge theory of gravity are completely the same as those given by general relativity.

Mechanics analysis of vehicle bumping at approach slabs with superelevation

In order to analyze the pavement stress caused by vehicle bumping at an approach slab, a simplified four-wheeled bi- axle vehicle-moving model is proposed. The effect of damping and vibration reduction in the process of vehicle-moving is not considered. Based on the position change of vehicle wheels at the approach slab, the vehicle dynamic vibration equations are summarized. Meanwhile, the undetermined coefficients of the vibration equations are obtained using the boundary and initial conditions of the vehicle. The analytical motion solutions of rear and front wheels at different stages are concluded. Consequently, a four-wheeled vehicle model is developed and vibration equations are provided, which can be used to analyze the impact of complicated stress on pavement. The results show that the excessive stress and stress concentration will occur at the approach slab, and it needs to be strengthened.

Nonlinear dynamics of fixed-trim reentry vehicles with moving-mass roll control system

Nonlinear dynamic characteristics of a fixed-trim reentry vehicle controlled by an internal moving-mass actuator are analyzed. A traditional dynamic model develops into a five-dimensional nonlinear model using classic Euler angles and their derivatives as state variables. Based on the nonlinear motion equations, by setting the offset distance of the moving-mass as a variation parameter, the curves of the system's equilibrium points are presented by numerical methods. Then the distributions and approximate analytical solutions of the equilibrium points are obtained by simplifying the model under the condition of small intrinsic angles. The results show that the numbers and values of the equilibrium points are closely connected with the location of the moving-mass. Furthermore, the stabilities of equilibrium points are examined by the Lyapunov's first method and three groups of stable equilibrium points are obtained. Since only one group of the stable equilibrium points is desired, the angular motion of the system may be unstable or stay in an undesired lock-in state when the offset distance of the moving-mass or the attitude disturbance of the vehicle is too large. © 2016 Beijing Institute of Aerospace Information.

Dynamics of vehicles with high gravity centre

The vehicles with high gravity centre are more prone to roll over. The paper deals with a method of dynamics analysis of fire engines which is an example of these types of vehicle. Algorithms for generating the equations of motion have been formulated by homogenous transformations and Lagrange＇s equation. The model presented in this article consists of a system of rigid bodies connected one with another forming an open kinematic chain. Road maneuvers such as a lane change and negotiating a circular track have been presented as the main simulations when a car loses its stability. The method has been verified by comparing numerical results with results obtained by experimental measurements performed during road tests.

固定翼UAV路径跟踪的全局稳定积分滑模S面控制

针对固定翼无人机的三维路径跟踪控制问题,设计了一种基于全局稳定积分滑模S面模型的内外环控制器。控制器外环采用全局稳定积分滑模控制,内环采用S面控制。设计控制器外环的全局稳定积分滑模控制律,并采用Lyapunov理论证明所设计控制律的稳定性。对内环的指令信号设计S面控制器,考虑到S面控制器中求导的复杂性,引入二阶微分器,解决内环中导数存在积分爆炸的问题。半物理仿真试验结果表明,提出的控制器能精确跟踪期望路径,具有良好的控制性能和抗干扰性能。

专家控制-改进S面算法在近水面航行器运动控制中的应用研究

[目的]旨在提高舵板响应速度和效率,以满足近水面航行器在静水及波浪干扰下的深度保持和姿态控制要求。[方法]在S面算法的基础上,提出一种具有更快收敛速度的改进S面控制算法,并与专家智能控制相结合,建立闭环专家控制-改进S面算法的混合控制模型,构建混合算法控制器。对比分析PID算法、S面算法、改进S面算法以及专家控制-改进S面算法在近水面航行器航行深度、姿态控制间的差异,并进行波浪干扰下的运动预报。[结果]预报结果表明:改进S面算法在静水航行控制中可提高收敛速度,波浪干扰下可降低纵摇幅度;专家控制-改进S面算法能够提高舵的控制效率,在静水中快速实现航行状态稳定转换,在波浪中有效降低近水面航行器垂荡和纵摇幅值30%以上。[结论]所提专家控制-改进S面算法对近水面航行器运动稳定性的提高适用性良好。

Bernoulli’s Equation with Acceleration

For steady frictionless flow along a straight line, when a constant acceleration is applied parallel to that line, a term needs to be added to the standard form of Bernoulli’s equation. After so modifying, the equation then predicts that along a streamline, when the speed is high, the pressure is significantly lower than that if there were no acceleration. For example, one might think of a dense fluid falling down through a less dense fluid under gravity. Potential applications to vertical motions of the atmosphere, such as down bursts of cold dry air and warm humid updrafts in the eye of a hurricane, are mentioned.

A Solution of Kepler’s Equation

The present study deals with a traditional physical problem: the solution of the Kepler’s equation for all conics (ellipse, hyperbola or parabola). Solution of the universal Kepler’s equation in closed form is obtained with the help of the two-dimensional Laplace technique, expressing the universal functions as a function of the universal anomaly and the time. Combining these new expressions of the universal functions and their identities, we establish one biquadratic equation for universal anomaly (χ) for all conics;solving this new equation, we have a new exact solution of the present problem for the universal anomaly as a function of the time. The verifying of the universal Kepler’s equation and the traditional forms of Kepler’s equation from this new solution are discussed. The plots of the elliptic, hyperbolic or parabolic Keplerian orbits are also given, using this new solution.

MOTION VELOCITY SMOOTH LINK IN HIGH SPEED MACHINING

To deal with over-shooting and gouging in high speed machining, a novel approach for velocity smooth link is proposed. Considering discrete tool path, cubic spline curve fitting is used to find dangerous points, and according to spatial geometric properties of tool path and the kinematics theory, maximum optimal velocities at dangerous points are obtained. Based on method of velocity control characteristics stored in control system, a fast algorithm for velocity smooth link is analyzed and formulated. On-line implementation results show that the proposed approach makes velocity changing more smoothly compared with traditional velocity control methods and improves productivity greatly.

Brownian Motion of Decaying Particles: Transition Probability, Computer Simulation, and First-Passage Times

Recent developments in the measurement of radioactive gases in passive diffusion motivate the analysis of Brownian motion of decaying particles, a subject that has received little previous attention. This paper reports the derivation and solution of equations comparable to the Fokker-Planck and Langevin equations for one-dimensional diffusion and decay of unstable particles. In marked contrast to the case of stable particles, the two equations are not equivalent, but provide different information regarding the same stochastic process. The differences arise because Brownian motion with particle decay is not a continuous process. The discontinuity is readily apparent in the computer-simulated trajectories of the Langevin equation that incorporate both a Wiener process for displacement fluctuations and a Bernoulli process for random decay. This paper also reports the derivation of the mean time of first passage of the decaying particle to absorbing boundaries. Here, too, particle decay can lead to an outcome markedly different from that for stable particles. In particular, the first-passage time of the decaying particle is always finite, whereas the time for a stable particle to reach a single absorbing boundary is theoretically infinite due to the heavy tail of the inverse Gaussian density. The methodology developed in this paper should prove useful in the investigation of radioactive gases, aerosols of radioactive atoms, dust particles to which adhere radioactive ions, as well as diffusing gases and liquids of unstable molecules.

Hamiltonian Formulation for Water Wave Equation

This paper concerns the development and application of the Hamiltonian function which is the sum of kinetic energy and potential energy of the system. Two dimensional water wave equations for irrotational, incompressible, inviscid fluid have been constructed in cartesian coordinates and also in cylindrical coordinates. Then Lagrangian function within a certain flow region is expanded under the assumption that the dispersion μ and the nonlinearity ε satisfied . Using Hamilton’s principle for water wave evolution Hamiltonian formulation is derived. It is obvious that the motion of the system is conservative. Then Hamilton’s canonical equation of motion is also derived.

AUV Load Separation Motion with Constraint of Anchor Chain

Motion equations of AUV(autonomous underwater vehicle) load separation with the constraint of anchor chain is derived.Based on proper engineering assumptions for anchor chain,system viewpoint is used to found the motion equations,and the D'Alembert principle is used to eliminate the constraint force of anchor chain.Based on the equations,the motion simulation is carried out to a certain AUV,which reflects the actual condition,and is used for the reference of resrarching AUV load separation motion with the constraint of anchor chain.

An Extented Wave Action Equation

Based on the Navier-Stokes equation, an average wave energy equation and a generalized wave action conservation equation are presented in this paper. The turbulence effects on water particle velocity u i and wave surface elavation ξ as well as energy dissipation are included. Some simplified forms are also given.

Canards Flying on Bifurcation

There exists a property “structural stability” for “4-dimensional canards” which is a singular-limit solution in a slow-fast system with a bifurcation parameter. It means that the system includes the possibility to have some critical values on the bifurcation parameter. Corresponding to these values, the pseudo-singular point, which is a singular point in the time-scaled-reduced system should be changed to another one. Then, the canards may fly to another pseudo-singular point, if possible. Can the canards fly? The structural stability gives the possibility for the canards flying. The precise reasons why happen are described in this paper.

水下机器人自适应S面控制

以某机器人为研究对象,使用S(Sigmoid)面控制方法构造了速度控制器并分析了该控制器的稳定性.参考滑模变结构控制思想,提出了参数自适应S面速度控制器,使控制参数根据运动状态自适应调整.同时,为了提高S面位置控制器的适应性,改进了控制器的自适应调整项,增强了控制器消除稳态误差的能力,实现了S面控制器局部动态调整.水池中的对比实验和海洋验证实验表明,改进方法获得了良好的控制效果,有效提高了水下机器人运动控制的适应性.

改进的模拟退火算法在水下机器人S面运动控制参数优化中的应用

从模糊逻辑控制思想出发,借鉴PID控制的结构而设计的S面控制器,其控制方法调整参数少,是一种简单实用的水下机器人运动控制方法,但其控制参数需要手工调整。针对S面方法由于控制参数设置不当,严重影响水下机器人运动控制精度与效果的问题,提出一种基于改进的模拟退火算法来优化S面运动控制参数的方法。通过对初始温度的选择、退火算法、增加记忆功能、停止温度的设定等方面改进了模拟退火算法,利用该算法进行水下机器人S面控制器参数的寻优与优化,可以实现控制参数的自动调整。试验结果表明基于模拟退火参数优化的S面控制方法优于普通S面控制方法,具有更好的控制精度,更快的响应速度。

基于简化Mumford-Shah模型的导航基准图适配区分割方法

基于景象匹配的飞行器导航数字基准地图中需要划分匹配稳定的区域,以提高导航系统航迹的可靠性.该文首先讨论了描述基准图局部区域匹配稳定性的局部匹配稳健度量指标,据此定义了适配区的概念.常规的基于相关函数局部匹配稳健度量需要大量的计算时间,难以实用化.为此,文中采用了三种可快速计算的匹配稳健度量指标:相关主峰曲率、可跟踪度及特征密度,以及相应的快速算法.同时,引入了一种基于简化Mumford-Shah模型的水平集算法进行适配区划分,通过演化由模型推导出的偏微分方程,就能得到适配区和非适配区的最优划分.最后对实际的导航基准图的适配区划分试验表明,该文的适配区分割方法不仅计算速度优于基于相关函数的方法,而且可以获得合理的适配区分布.

日本海沟俯冲带海底地震动累积能量参数的条件预测模型

阿里亚斯强度(IA)、累积绝对速度(CAV)和峰值地面加速度(PGA)已被广泛用作地震动强度的评价指标.为了研究海底地震动特征及其能量累积效应,采用日本海沟区域的138次浅地壳地震的2605组三分量记录、125次俯冲板内地震的2669组三分量记录和267次俯冲板间地震的5693组三分量记录来建立IA-PGA和CAV-PGA条件模型,并研究其对震级(MW)、震源机制、断层距(Rrup)、海水深度(DW)以及剪切波速(VS)等于1.5 km·s^(-1)的深度(D15)等解释变量的潜在依赖性.基于条件模型,建立了海域的IA和CAV地震动预测方程(GMPE).研究结果表明:各个解释变量对条件模型有着不同影响,震级为主要影响因素;震级对海域的能量累积效应影响较大,随着震级增大,能量累积效应越大.通过基于条件模型得到IA和CAV预测模型与现有陆域的IA和CAV模型进行了比较,在相同震级和距离下,海域的能量累积效应要大于陆域.本文提供了海域的从PGA估算IA、CAV的方法,能用于损伤预测和评估、地震预警(EEW)和海啸预警等.