理论力学碰撞19.ppt

1 　 (1)The conventional forces are much smaller than the forces of impact ,they can be neglected during the impact. (2) The displacement of the points of a body during the time of impact can be neglected . (1) 在碰撞过程中，普通力远小于碰撞力，可以忽略不计； (2) 物体在碰撞过程中不发生位移。 3、研究碰撞问题的两个基本定理是冲量定理和冲量矩定理。 3.Two fundamental theorems for impact problems are the theorem of impulse and the theorem of the moment of the impulse. 4、两物体碰撞的恢复系数 k 等于碰撞结束和开始时，两物体接触点沿公法线方向相对速度大小的比值。 4.The co efficient of restitution k during an impact of two bodies equals to the ratio of the absolute values of the relative velocities of the two bodies along the common nomal at the end of impact to that at the beginning of the impact . 　 Au impact is called to be a perfectly elastic one if k=1.In the of k=0 if is called a perfectly inelastic or a plastic one. 0k 1 为弹性碰撞，k =1为完全弹性碰撞，k =0为非弹性碰撞或塑性碰撞。 5. There is a loss of kinetic energy during an impact ，the magnitude of which depends on the value of the coefficient of restitution . 5、在碰撞过程中有动能损失，动能损失的多少取决于恢复系数k 值的大小。 　 6、作用于绕定轴转动刚体上的外碰撞冲量将引起刚体角速度的突变，并引起轴承的反碰撞冲量。 6.An external impact impulse acting on a rigid body rotating about a fixed axis will causes a sharp change of the angular velocity of the body and reaction forces at the bearings . 当外碰撞冲量作用在刚体的垂直于转轴的对称面内的撞击中心，且垂直于质心与轴心的连线时，可使轴承的反碰撞冲量等于零。 The reaction forces at the bearings equal to zero if the external impact impulse lies in the plane of symmetry perpendicular to the axis of rotation and is applied to the center of impact and directed perpendicular to the plane through the axis of rotation and the center of mass of the body . 　 　 Please look at the animation 请看动画 The velocities of the two centers of mass at the end of the direct impact 1、正碰撞结束时两质心的速度 Example：The velocities of the approach of two colliding bodies are and . The velocities of their separation are denoted by and (alon