Theoretical mechanics anter basic motions of a rigid body
1 Theoretical mechanics
理论力学
2
Chapter 7: Basic motions of a rigid body ED 87-1 Translational motion of a rigid body ED 8 7-2 Rotation of a rigid body about a fixed axis D 87-3 Velocity and acceleration of a point in a rigid body rotating about a fixed axis D87-4 Transmission between two rotating rigid bodies D 87-5 Vector representation of angular velocity and angular acceleration E Lesson for problem solving
3 §7–1 Translational motion of a rigid body §7–2 Rotation of a rigid body about a fixed axis §7–3 Velocity and acceleration of a point in a rigid body rotating about a fixed axis §7–4 Transmission between two rotating rigid bodies §7–5 Vector representation of angular velocity and angular acceleration Lesson for problem solving Chapter 7: Basic motions of a rigid body
第七章刚体的基本运动 P§7-1刚体的平行移动 §7-2刚体的定轴转动 §7-3定轴转动刚体内各点的速度与加速度 國§7-4绕定轴转动刚体的传动问题 F§7-5角速度与角速度的矢量表示 点的速度与加速度的矢积表示 习题课
4 §7–1 刚体的平行移动 §7–2 刚体的定轴转动 §7–3 定轴转动刚体内各点的速度与加速度 §7–4 绕定轴转动刚体的传动问题 §7–5 角速度与角速度的矢量表示 点的速度与加速度的矢积表示 习题课 第七章 刚体的基本运动
means Chapter 7: Basic motions of a rigid body Examples translation and Basic motions rotation 直线平动 出线平动 定轴转动 Rectilinear translation curvilinear translation Rotation about a fixed axis 87-1 Translational motion of a rigid body The shape and dimensions of a rigid body should be considered investigating its motion. However, due to its unchanged shape
5 Chapter 7: Basic motions of a rigid body The shape and dimensions of a rigid body should be considered investigating its motion. However,due to its unchanged shape,. §7-1 Translational motion of a rigid body [Examples] translation and rotation Basic motions Rectilinear translation curvilinear translation Rotation about a fixed axis
运动学 第七章刚体的基本运动 [例] 是指刚体的平行一基本运动 移动和转动 出线平动 定轴转动 直线平动 §7-1刚体的平行移动(平动) 由于研究对象是刚体,所以运动中要考虑其本身形状和尺 寸大小,又由于刚体是几何形状不变体,所以研究它在空间的
6 第七章 刚体的基本运动 [例] 由于研究对象是刚体,所以运动中要考虑其本身形状和尺 寸大小,又由于刚体是几何形状不变体,所以研究它在空间的 是指刚体的平行 移动和转动 §7-1刚体的平行移动(平动) 基本运动
Kinematics It is not necessary to determine its position by finding the positions of all its points. Instead, its position is determined completely by c describing the position of a line or a plane in it B y A OB rotates about a fixed axis The motions of ab and of The motion of cd is a translation the cam are translations
7 OB rotates about a fixed axis The motion of CD is a translation The motions of AB and of the cam are translations It is not necessary to determine its position by finding the positions of all its points. Instead, its position is determined completely by describing the position of a line or a plane in it
运动学 位置就不必一个点一个点地确定,只要根据刚体的各种运动形 式,确定刚体内某一个有代表性的直线或平面的位置即可。 B D OB作定轴转动 CD作平动 AB、凸轮均作平动 8
8 OB作定轴转动 CD作平动 AB、凸轮均作平动 位置就不必一个点一个点地确定,只要根据刚体的各种运动形 式,确定刚体内某一个有代表性的直线或平面的位置即可
Kinematics Example The length and direction ofaB B do not change at all during its B B motion B A A Its trajectory may be a straight line a curve I. Definition of translatory motion of a rigid body: The direction of the line linking arbitrary two points in the rigid body never changes during its motion Note the equations of motion of the points a andB, i.e. ra=rA(t), rB=rB(t) and rn=r+r AB we have A B B +FAB)=,4=(∵ 0) dt d St ly B B dt 2 dt 2(4+4B)= t
9 = = ( + ) = = ( = 0) dt dr v dt dr r r dt d dt dr v A B A A A A B B B 1. Definition of translatory motion of a rigid body: The direction of the line linking arbitrary two points in the rigid body never changes during its motion. Note the equations of motion of the points A and B, i.e. and ,we have r r ( t),r r (t) A = A B = B B A AB r =r +r A A A A B B B a dt d r r r dt d dt d r Similarly a = = + = = 2 2 2 2 2 2 , ( ) The length and direction of AB do not change at all during its motion. Its trajectory may be a straight line a curve [Example]
动学 例] B 丕B在运动中方向和大小始 B 1)终不变 AB A 可以是直线 A 它的轨迹 可以是曲线 刚体平动的定义: 刚体在运动中,其上任意两点的连线始终保持方向不变 由A,B两点的运动方程式:FA=(D,B=B(1)而B=FA+FAB ∴n=Bd A B dt dt A千AB drA=vAdt dt =0) 2 同理aB=2=2(r4+FB) 12A=0A 10
10 = = ( + )= = ( =0) dt dr v dt dr r r dt d dt dr v A B A A A A B B B 一.刚体平动的定义: 刚体在运动中,其上任意两点的连线始终保持方向不变。 由A,B 两点的运动方程式: r A =r A ( t),r B =r B (t) 而 B A AB r =r +r A A A A B B B a dt d r r r dt d dt d r a = = + = = 2 2 2 2 2 2 同理: ( ) [例] AB在运动中方向和大小始 终不变 它的轨迹 可以是直线 可以是曲线