刚体一般运动的描述

刚体的一般运动是刚体运动学中最复杂的一类运动,其求解通常需要借助欧拉定理或沙勒定理.通过这两个定理,我们可以把刚体的一般运动分解成较简单的定轴转动和平动.本文主要应用代数理论中的正交矩阵描述刚体的运动,并用代数语言分析了定点转动的本征问题,证明了欧拉定理.随后,将刚体的定点转动进行分解,并给出了物理图像和推导结论,完成了对刚体复杂的一般运动的简单描述.     

Rigid Body Motion in Special Relativity

We study the acceleration and collisions of rigid bodies in special relativity. After a brief historical review, we give a physical definition of the term ‘rigid body’ in relativistic straight line motion. We show that the definition of ‘rigid body’ in relativity differs from the usual classical definition, so there is no difficulty in dealing with rigid bodies in relativistic motion. We then describe

1. The motion of a rigid body undergoing constant acceleration to a given velocity.
2. The acceleration of a rigid body due to an applied impulse.
3. Collisions between rigid bodies.

     

Relative equilibria for the generalized rigid body

This paper gives necessary and sufficient conditions for the (n-dimensional) generalized free rigid body to be in a state of relative equilibrium. The conditions generalize those for the case of the three-dimensional free rigid body, namely that the body is in relative equilibrium if and only if its angular velocity and angular momentum align, that is, if the body rotates about one of its principal axes. For the n-dimensional rigid body in the Manakov formulation, these conditions have a similar interpretation. We use this result to state and prove a generalized Saari’s Conjecture (usually stated for the N-body problem) for the special case of the generalized rigid body.     

New integrable problem of classical mechanics

Complete integrability in Liouville's sense is proven for rotation of an arbitrary rigid body with a fixed point in a Newtonian field with an arbitrary homogeneous quadratic potential. A consequences is the complete integrability of rotation of a rigid body with fixed center of mass in the field of arbitrary sufficiently remote objects (in the second approximation). Explicit formulae are obtained expressing angular velocities of the rigid body in terms of -functions for Riemannian surfaces. Integrable cases are found for rotation of a rigid body in nonlinear Newtonian potential fields.     

利用刚体转动惯量实验仪验证转动定律的设计

介绍了设计性实验“利用刚体转动惯量实验仪验证转动定律”.该实验要求学生理解刚体动力学原理;利用实验室现有的仪器,对刚体转动惯量实验仪进行改装;提出新的实验原理,可以对阻力矩进行估测,利用该实验装置验证刚体定轴转动定律.     

Technique for compensating excessive rigid body motion in nondestructive testing of large structures using shearography

A major limitation of speckle interferometry techniques including shearography is that the occurrence of rigid body motion produces a decorrelation of speckle patterns which destroys the fringe visibility. This paper demonstrates that digital shearography can tolerate much greater rigid body translation than a speckle size as predicted by the conventional speckle decorrelation theory. Excessive rigid body translation in digital shearography can be compensated by either translating the sensor/camera or digitally shifting one of the speckle patterns.     

刚体定点转动的张量描述

通过引入转动张量来描述刚体的定点转动,避免了在用角位移描述刚体定点转动时所遇到的问题,即角位移在它是有限大小和无限小时属性发生了变化.验证了对于刚体定点无限小转动,可以分别采用角位移矢量和转动张量描述,两者是等价的.     

用三线摆研究垂直轴定理

用三线摆对刚体薄圆盘绕不同轴转动时的转动惯量进行测量,通过实验与数据分析,验证了反映刚体转动惯量重要性质的垂直轴定理,从而实现了对刚体转动惯量实验内容的扩充.     

刚体运动对云纹干涉法的影响

本文详细讨论了试件在空间六个自由度中产生刚体运动时所形成的云纹图特性，定量地分析了各种刚体运动形式对云纹干涉法的影响。经分析表明：在用云纹干涉法测量变形位移场时，只有当试件绕坐标轴刚体转动时才会影响所测变形位移场。     

Rigid Body Inertia Properties

Russian Physics Journal - Definitions are given and properties of the rigid body inertia characteristics are formulated. The influence of the geometrical symmetry of a rigid body on its...     

Vibration analysis of a new curved beam element

The common practice in developing a locking-free curved beam element is to ensure that its interpolation functions of displacement explicitly satisfy the inextensible bending mode condition for the membrane locking-free instead of the rigid body modes. In this paper, we study the impact of this practice on the dynamic characteristics of a finite element by conducting vibration analysis using our newly developed three-node locking-free curved beam element. In this case, the inextensible bending mode condition is satisfied explicitly, while the rigid body modes are satisfied implicitly to 4th-order accuracy. Numerical and experimental examples show that with the newly developed curved beam element, developed by using the implicit representation of a rigid body mode condition, it is possible to recover the rigid body modes of curved beams with low and medium slenderness ratios. This is even true for cases involving a half-circular element and the vibration of the curved beam is predicted with high accuracy.     

巧用类比教学法实现刚体力学的有效教学简

巧妙地运用类比教学法对刚体力学和质点力学的物理概念、物理规律、公式以及解决问题的思路和方法等方面列表逐一分析、探究。部分测验成绩表明,巧用类比教学法,能提高刚体力学部分学业成绩,从而实现了刚体力学的有效教学。     

刚性细杆上的共轭点

从子弹射杆问题引出刚性细杆上的共轭点及其动力学性质,给出共轭点应用的几个例子,指出可以将共轭点的概念推广到刚性薄片和一般刚体情形．     

Motion of a body along a plane under the influence of movable internal masses

The two-dimensional horizontal plane motion of a rigid body with internal movable masses and dry friction forces acting between the body and the plane is considered. It is demonstrated that, under certain conditions, this rigid body may be transferred from the given initial position to the given end position by means of movement of the internal masses.     

非完整映射理论与刚体定点转动的几何描述

利用非完整映射方法,从一个已知Riemann空间构造一个嵌入其中的Riemann-Cartan空间.作为特例,研究从Euclidean空间构造Weitzenbock空间的方法.基于dAlembert-Lagrange原理和非完整映射,将一个Riemann空间的测地线对应于另一个Riemann-Cartan空间的自平行线.把这种非完整映射理论应用到刚体定点转动问题上,得到了刚体运动的欧拉方程是欧拉角描述的Riemann位形空间的测地线方程,而在刚体角速度对应的准坐标空间上是常挠率Riemann-Cartan空间的自平行线方程的结论. 关键词： 欧拉角 非完整映射 Riemann-Cartan空间 自平行线     

均质并有对称面的刚体转动惯量的一个定理

提出并证明了一个关于刚体转动惯量的新定理.该定理指出具有对称面的均质刚体,当位于与对称面垂直的某个平面上的转轴满足特定条件时,转动惯量大小与位于该平面上的转轴方向无关.     

Application of stereo vision to the study of mixed-mode crack-tip deformations

A stereo vision is applied to evaluate crack-tip parameters for fracture specimens subjected to a mixed-mode loading (tension and shear). By using a special loading device, the applied remote loading is oriented at an angle with respect to the axis of the crack. At each loading angle, the calibrated vision system was rotated so that the axis of the crack is parallel to the horizontal or vertical axis of the image frame. At a load close to the crack initiation, the displacement field around the crack-tip region of the fracture specimen was measured relative to a specimen coordinate system located at the crack tip of the fracture specimen. During the experiment, the fracture specimen was subjected to rigid body translation and rotation. Hence, the displacement fields are affected by the rigid body translation and rotation. Using the experimentally determined displacements and the analytically determined displacements with several higher order terms being included, the stress intensity factors and the amount of rigid body translation and rotation were calculated through a least-squares fit. The effect of the rigid body motion on the measured displacements was then eliminated using the computed rigid body translation and rotation. Experimental results indicate that a K_I and K_II dominant region is observed in the corrected displacement fields.     

对刚体动平衡校正实验仪的研制

本文介绍了对刚体动平衡量的准确、快速测量的一种方法,以及刚体动平衡校正实验仪的基础结构及原理。     

Periodic orbits around the collinear libration points in the restricted three body problem when the smaller primary is a triaxial rigid body and bigger primary is a source of radiation pressure

Periodic orbits belonging to the stromgren families A, B and C around the collinear libration points in the restricted three body problem have been studied when the smaller primary is a triaxial rigid body and more massive body is a source of radiation pressure. These families are determined in three different cases: (i) classical case, (ii) when bigger primary is a source of radiation pressure, (iii) when smaller primary is a triaxial rigid body and bigger primary is a source of radiation pressure. The Liapunov stability of each periodic solution has also been examined.