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.

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.

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.

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

Bifurcation of Periodic Motion of Rigid Rotor System Supported by Angular Contact Ball Bearings

Rotor systems supported by angular contact ball bearings are complicated due to nonlinear Hertzian contact force. In this paper, nonlinear bearing forces of ball bearing under five-dimensional loads are given, and 5-DOF dynamic equations of a rigid rotor ball bearing system are established. Continuation-shooting algorithm for periodic solutions of the nonlinear non-autonomous dynamic system and Floquet multipliers of the system are used. Furthermore, the bifurcation and stability of the periodic motion of the system in different parametric domains are also studied. Results show that the bifurcation and stability of period-1 motion vary with structural parameters and operating parameters of the rigid rotor ball bearing system. Avoidance of unbalanced force and bending moment, appropriate initial contact angle, axial load and damping factor help enhance the unstable rotating speed of period-1 motion.

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。

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%。

刚体平面运动中坐标轴正方向的选取

平面运动作为刚体的一种重要运动类型,成为物理学专业力学和理论力学课程中的重点教学内容.平面运动因为同时涉及平动和定轴转动且二者之间常常存在一定的约束关系,所以也是一个教学难点,主要问题在于初学者往往因为随意规定坐标轴正方向而遗漏约束关系中可能出现的负号.根据受力分析,在假定了刚体平面运动趋势后,适当选取坐标轴的正方向可以避开约束方程中的负号,从而使学生分析刚体运动问题更加快速准确.

近断层地震作用下高速铁路大跨连续刚构桥易损性研究

为探究近断层地震作用下高速铁路大跨连续刚构桥的抗震性能,基于工程需求(EDP)符合对数高斯分布假设获取全桥损伤曲线,提出一种桥梁地震损伤危险性分级方法。在此基础上,考虑桥上无砟轨道的刚度效应,采用OpenSees有限元软件建立了某高速铁路大跨连续刚构桥的轨道-桥梁(线-桥)一体化非线性有限元模型;由80条近断层地震动实录波组成地震动数据库,采用基于概率需求的易损性分析方法详细分析了该高速铁路大跨连续刚构桥的抗震性能。结果表明:对于研究计算条件,近断层地震动速度峰值(PGV)与工程需求间的相关性较强;近断层地震作用下高速铁路连续刚构桥的边支座易出现轻微损伤,当遭遇中高强度(PGV>100 cm/s)近断层地震动时桥梁关键截面的屈服概率较大,当PGV为200 cm/s时桥梁结构会受到严重破坏,而当PGV为300 cm/s时桥梁有极大可能发生完全破坏甚至出现倒塌。研究成果可为近断层区域高速铁路连续刚构桥的抗震设计提供参考。

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.