AN UNCERTAINTY PRINCIPLE ON THE GROUP OF RIGID MOTIONS OF THE PLANE

Let M(2)be the group of rigid motions of the plane.The Fourier transform and the Piancherel formula on M(2)can be explicitly given by the general group representation theory.Using this fact.we establish a kind of uncertainty principle on M(2).The result can easily be generalized to higher dimensional cases.An application of the result yields an uncertainty principle on the Euclidean spaces obtained by R.S.Strichartz.

Amended influence matrix method for removal of rigid motion in the interior BVP for plane elasticity

A conventional complex variable boundary integral equation （CVBIE） in plane elasticity is provided. After using the Somigliana identity between a particular fundamental stress field and a physical stress field, an additional integral equality is obtained. By adding both sides of this integral equality to both sides of the conventional CVBIE, the amended boundary integral equation （BIE） is obtained. The method based on the discretization of the amended BIE is called the amended influence matrix method. With this method, for the Neumann boundary value problem （BVP） of an interior region, a unique solution for the displacement can be obtained. Several numerical examples are provided to prove the efficiency of the suggested method.

Gauss-Bonnet theorems in the affine group and the group of rigid motions of the Minkowski plane

In this paper,we compute sub-Riemannian limits of Gaussian curvature for a Euclidean C^(2)-smooth surface in the affine group and the group of rigid motions of the Minkowski plane away from characteristic points and signed geodesic curvature for Euclidean C^(2)-smooth curves on surfaces.We get Gauss-Bonnet theorems in the affine group and the group of rigid motions of the Minkowski plane.

Open-plus-closed-loop control for chaotic motion of 3D rigid pendulum

An open-plus-closed-loop （OPCL） control problem for the chaotic motion of a 3D rigid pendulum subjected to a constant gravitationM force is studied. The 3D rigid pendulum is assumed to be consist of a rigid body supported by a fixed and frictionless pivot with three rotational degrees. In order to avoid the singular phenomenon of Euler＇s angular velocity equation, the quaternion kinematic equation is used to describe the motion of the 3D rigid pendulum. An OPCL controller for chaotic motion of a 3D rigid pendulum at equilibrium position is designed. This OPCL controller contains two parts： the open-loop part to construct an ideal trajectory and the closed-loop part to stabilize the 3D rigid pendulum. Simulation results show that the controller is effective and efficient.

ON UNILATERALLY CONSTRAINED MOTIONS OF RIGID BODIES SYSTEMS

In this paper , the unilaterally constrained motions of a large class of rigid bodiessystems are studied both locally and globally. The main conclusion is that locally,such a system bahaves like a particle in a Riemannian manifold with boundary;globally.under the assumption of energy conservation, the system behaves like a billiards system over a Riemannina manifold with boundary

Monolithic Coupling of the Pressure and Rigid Body Motion Equations in Computational Marine Hydrodynamics

In Fluid Structure Interaction(FSI) problems encountered in marine hydrodynamics, the pressure field and the velocity of the rigid body are tightly coupled. This coupling is traditionally resolved in a partitioned manner by solving the rigid body motion equations once per nonlinear correction loop, updating the position of the body and solving the fluid flow equations in the new configuration. The partitioned approach requires a large number of nonlinear iteration loops per time–step. In order to enhance the coupling, a monolithic approach is proposed in Finite Volume(FV) framework,where the pressure equation and the rigid body motion equations are solved in a single linear system. The coupling is resolved by solving the rigid body motion equations once per linear solver iteration of the pressure equation, where updated pressure field is used to calculate new forces acting on the body, and by introducing the updated rigid body boundary velocity in to the pressure equation. In this paper the monolithic coupling is validated on a simple 2D heave decay case. Additionally, the method is compared to the traditional partitioned approach(i.e. "strongly coupled" approach) in terms of computational efficiency and accuracy. The comparison is performed on a seakeeping case in regular head waves, and it shows that the monolithic approach achieves similar accuracy with fewer nonlinear correctors per time–step. Hence, significant savings in computational time can be achieved while retaining the same level of accuracy.

MOTION AND DEFORMATION OF VISCOUS DROP IN STOKES FLOW NEAR RIGID WALL

A boundary integral method was developed for simulating the motion and deformation of a viscous drop in an axisymmetric ambient Stokes flow near a rigid wall and for direct calculating the stress on the wall. Numerical experiments by the method were performed for different initial stand-off distances of the drop to the wall, viscosity ratios, combined surface tension and buoyancy parameters and ambient flow parameters. Numerical results show that due to the action of ambient flow and buoyancy the drop is compressed and stretched respectively in axial and radial directions when time goes. When the ambient flow action is weaker than that of the buoyancy the drop raises and bends upward and the stress on the wall induced by drop motion decreases when time advances. When the ambient flow action is stronger than that of the buoyancy the drop descends and becomes flatter and flatter as time goes. In this case when the initial stand-off distance is large the stress on the wall increases as the drop evolutes but when the stand-off distance is small the stress on the wall decreases as a result of combined effects of ambient flow, buoyancy and the stronger wall action to the flow. The action of the stress on the wall induced by drop motion is restricted in an area near the symmetric axis, which increases when the initial stand-off distance increases. When the initial stand-off distance increases the stress induced by drop motion decreases substantially. The surface tension effects resist the deformation and smooth the profile of the drop surfaces. The drop viscosity will reduce the deformation and migration of the drop.

PERIODIC MOTIONS OF SPINNING RIGID SPACECRAFT UNDER INFLUENCE OF GRAVITATIONAL AND MAGNETIC FIELDS

The motion of a magnetized axisymmetric spacecraft about its center of mass in a circular orbit is considered, taking the gravitational and magnetic effects of the central body into account. Equations of motion of the reduced system are transformed to equations of plane motion of a charged particle under the action of electric and magnetic fields. Stationary motions of the system are determined and periodic motions near to them are constructed using the Lyapounoff theorem of the holomorphic integral.

A Robust Incremental Algorithm for Predicting the Motion of Rigid Body in a Time-Varying Environment

A configuration point consists of the position and orientation of a rigid body which are fully described by the position of the frame’s origin and the orientation of its axes, relative to the reference frame. We describe an algorithm to robustly predict futuristic configurations of a moving target in a time-varying environment. We use the Kalman filter for tracking and motion prediction purposes because it is a very effective and useful estimator. It implements a predictor-corrector type estimator that is optimal in the sense that it minimizes the estimated error covariance. The target motion is unconstrained. The proposed algorithm may be viewed as a seed for a range of applications, one of which is robot motion planning in a time-changing environment. A significant feature of the proposed algorithm (when compared to similar ones) is its ability to embark the prediction process from the first time step;no need to wait for few time steps as in the autoregressive-based systems. Simulation results supports our claims and demonstrate the superiority of the proposed model.

Terminal sliding mode control for coordinated motion of a space rigid manipulator with external disturbance

The control problem of coordinated motion of a free-floating space rigid manipulator with external disturbance is discussed. By combining linear momentum conversion and the Lagrangian approach, the full-control dynamic equation and the Jacobian relation of a free-floating space rigid manipulator are established and then inverted to the state equation for control design. Based on the terminal sliding mode control （SMC） technique, a mathematical expression of the terminal sliding surface is proposed. The terminal SMC scheme is then developed for coordinated motion between the base＇s attitude and the end-effector of the free-floating space manipulator with external disturbance. This proposed control scheme not only guarantees the existence of the sliding phase of the closed-loop system, but also ensures that the output tracking error converges to zero in finite time. In addition, because the initial system state is always at the terminal sliding surface, the control scheme can eliminate reaching phase of the SMC and guarantee global robustness and stability of the closed-loop system. A planar free-floating space rigid manipulator is simulated to verify the feasibility of the proposed control scheme.

OPTIMAL MOTION PLANNING FOR A RIGID SPACECRAFT WITH TWO MOMENTUM WHEELS USING QUASI-NEWTON METHOD

An optimal motion planning scheme based on the quasi-Newton method is proposed for a rigid spacecraft with two momentum wheels. A cost functional is introduced to incorporate the control energy, the final state errors and the constraints on states. The motion planning for determining control inputs to minimize the cost functional is formulated as a nonlinear optimal control problem. Using the control parametrization, one can transform the infinite dimensional optimal control problem to a finite dimensional one that is solved via the quasi-Newton methods for a feasible trajectory which satisfies the nonholonomic constraint. The optimal motion planning scheme was applied to a rigid spacecraft with two momentum wheels. The simulation results show the effectiveness of the proposed optimal motion planning scheme.

Introduction of Simulating the Motion of Rigid Ellipsoidal Objects in Ductile Shear Zone Based on the Jeffery's Theory

Rigid ellipsoidal objects(gravels and porphyroclasts)in ductile zone is an important factor to indicate the kinematics and dynamics.Jeffery’s theory(Jeffery G,1922),a quantitative research method,for the rotation ofthe rigid objects(no deformation)in the Newtonian fluid of the simple deformation field has been widely applied by geologists to the study of fabrics in rocks.The theory

Bionic Attitude Transformation Combined with Closed Motion for a Free Floating Space Robot

In order to realize the small error attitude transformation of a free floating space robot,a new method of three degrees of freedom（ DOF） attitude transformation was proposed for the space robot using a bionic joint. A general kinematic model of the space robot was established based on the law of linear and angular momentum conservation. A combinational joint model was established combined with bionic joint and closed motion. The attitude transformation of planar,two DOF and three DOF is analyzed and simulated by the model,and it is verified that the feasibility of attitude transformation in three DOF space. Finally,the specific scheme of disturbance elimination in attitude transformation is presented and simulation results are obtained.Therefore,the range of application field of the bionic joint model has been expanded.

MODEL OF CENTRIFUGAL EFFECT AND ATTITUDEMANEUVER STABILITY OF A COUPLEDRIGID-FLEXIBLE SYSTEM

The influences of nonlinear centrifugal force to large overall attitude motion of coupled rigid-flexible system was investigated. First the nonlinear model of the coupled rigid-flexible system was deduced from the idea of “centrifugal potential field', and then the dynamic effects of the nonlinear centrifugal force to system attitude motion were analyzed by approximate calculation; At last, the Lyapunov function based on energy norm was selected, in the condition that only the measured values of attitude and attitude speed are available, and it is proved that the PD feedback control law can ensure the attitude stability during large angle maneuver.

MODELING AND ANALYSIS OF A COUPLED RIGID_FLEXIBLE SYSTEM

Correct predictions of the behavior of flexible bodies undergoing large rigid-body motions and small elastic vibrations is a subject of major concern in the field of flexible multibody system dynamics. Because of failing to account for the effects of dynamic stiffening, conventional methods based on the linear theories can lead to erroneous results in many practical applications. In this paper, the idea of 'centrifugal potential field', which induced by large overall rotation is introduced, and the motion equation of a coupled rigid-flexible system by employing Hamilton's principle is established. Based on this equation, first it is proved that the elastic motion of the system has periodic property, then by using Frobenius' method its exact solution is obtained. The influences of large overall rigid motion on the elastic vibration mode shape and frequency are analysed through the numerical examples.

非刚体运动特征提取在武术运动中的应用

受光照与环境因素的影响,非刚体运动中的图像会存在视差干扰,导致非刚体运动特征提取效果不佳,因此提出一种针对非刚体运动的特征提取方法。对非刚体运动图像进行高斯滤波处理,在高斯差分尺度空间内,采用特征描述算子提取初始特征点。根据特征点提取结果,计算非刚体运动特征提取的代价。引入引导滤波方法对非刚体运动图像进行视差效果优化处理,在最小视差约束下,根据置信度聚合与传播策略进行非刚体运动的特征精确提取。以武术运动作为实验对象,实验结果表明:所提方法的特征点提取精度较高,且视差提取误差率不超过2.0%。

刚体定轴转动理论教学中的类比法应用研究

基于刚体定轴转动和质点直线运动具有较为类似的特点,文章主要研究类比法在刚体定轴转动理论教学过程的应用。对于经典运动的两大领域——运动学和动力学,在教学实施的过程中,利用二运动数学形式上的相似性和物理量之间内在的联系,将较为难懂的转动理论中的角量与学生所熟悉的质点直线运动中的线量进行类比,借助理解质点直线运动的思维模式,深入理解刚体定轴转动的各物理量以及相应的物理规律,从而为此部分内容的教学提供一套较为可行的简易化范式。

基于光流与多尺度上下文的图像序列运动遮挡检测

针对非刚性运动和大位移场景下运动遮挡检测的准确性与鲁棒性问题,提出一种基于光流与多尺度上下文的图像序列运动遮挡检测方法.首先,设计基于扩张卷积的多尺度上下文信息聚合网络,通过图像序列多尺度上下文信息获取更大范围的图像特征;然后,采用特征金字塔构建基于多尺度上下文与光流的端到端运动遮挡检测网络模型,利用光流优化非刚性运动和大位移区域的运动检测遮挡信息;最后,构造基于运动边缘的网络模型训练损失函数,获取准确的运动遮挡边界.分别采用MPI-Sintel和KITTI测试数据集对所提方法与现有的代表性方法进行实验对比与分析.实验结果表明,所提方法能够有效提高运动遮挡检测的准确性和鲁棒性,尤其在非刚性运动和大位移等困难场景下具有更好的遮挡检测鲁棒性.

考虑墩-梁碰撞效应的连续刚构桥系统易损性与概率地震风险性分析

为研究连续刚构桥主梁与过渡墩碰撞效应对其地震系统易损性和概率地震风险性的影响,以一座主桥跨径为(120+220+120)m的连续刚构桥为研究背景,通过模拟实际施工过程以获得真实成桥内力状态,基于等效荷载法建立考虑该内力状态的动力弹塑性分析模型,采用Hertz-damp接触模型考虑包括主梁与过渡墩碰撞在内的伸缩缝处碰撞效应。选取90条具有速度脉冲的脉冲型近断层地震动沿纵桥向输入,通过时程分析解释了墩梁碰撞过程和破坏机理;采用增量动力分析法,建立考虑桥墩和支座权重系数的全桥复合系统易损性曲线,并与一阶界限法串联模型下限和并联模型上限系统易损性曲线进行对比,将场地危险性函数与易损性函数卷积,建立概率地震风险曲线,考察桥梁系统易损性、概率地震风险性及墩梁碰撞效应的影响。结果表明,若忽略过渡墩与主桥梁体的碰撞效应,将会低估过渡墩的位移反应3~5倍,低估其地震风险性概率120%;当地震动强度为0.2g~0.6g时,轻微破坏和中等破坏的损伤概率被低估了35%~80%;地震动强度为0.6g~1.5g时,严重破坏和完全破坏分别被低估13%~68%和15%~59%。

飞机货舱门锁闩机构运动可靠性分析

飞机货舱门锁闩机构在舱门打开阶段协助提升电机进行舱门预位,磨损产生的铰链间隙会引起输出角度误差,降低锁闩机构运动可靠度。为了分析铰链磨损对于锁闩机构运动可靠度的影响,根据锁闩机构工作原理建立可靠度计算模型;建立货舱门刚柔耦合动力学模型计算铰链接触力;采用Archard磨损模型计算铰链磨损量,基于等效杆长理论将铰链磨损量转换成杆长变化量,建立参数化模型进行可靠度分析;利用孔销接触模型进行可靠度结果验证。结果表明:该可靠度分析方法能够保证计算精度,提高分析效率。