《理论力学 Theoretical Mechanics——静力学》PPT教学课件（双语）：第五章 空间力系 Force System in Space

Theoretical Mechanics Chapter 5? Force ytem in Space

1 Theoretical Mechanics

理论力学 第五二力系

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Statics Practically,there exists many force systems in which the action lines of the forces are not coplanar these are force systems in space They are the most general force systems Diagram(a)is a concurrent forces system in space Diagram(b)is an arbitrary force system in space, if neglecting the forces of the wind from the side it is a parallel force system in space The force of wind fren the front The force of(o P wind from the side (b)

3 Practically, there exists many force systems in which the action lines of the forces are not coplanar, these are force systems in space. They are the most general force systems. Diagram (a) is a concurrent forces system in space. Diagram (b) is an arbitrary force system in space, if neglecting the forces of the wind from the side it is a parallel force system in space. The force of wind from the front The force of wind from the side b

学 工程中常常存在着很多各力的作用线不在同一平面内的力 系,即空间力系,空间力系是最一般的力系 a)图为空间汇交力系;(b)图为空间任意力系 (b)图中去了风力为空间平行力系。 迎面 风力 侧面 P 风力 (b)

4 工程中常常存在着很多各力的作用线不在同一平面内的力 系，即空间力系，空间力系是最一般的力系。 (a)图为空间汇交力系；(b)图为空间任意力系； (b)图中去了风力为空间平行力系。 迎 面 风 力 侧 面 风 力 b

Chapter 5: Force system in space 85-1 Concurrent force system in space 85-2 System of force couples in space D85-3 The moment of a force about a point or an axis $5-4 Reduction of a force system in space to a given point 2$5-5 Discussion of the result of the reduction of a force system in space 85-6 Equilibrium equations of a force system in space and their applications D85-7 The center of a system of parallel forces and the center of gravity of an object Class of exercises

5 Chapter 5: Force system in space §5–1 Concurrent force system in space §5–2 System of force couples in space §5–3 The moment of a force about a point or an axis §5–4 Reduction of a force system in space to a given point §5–5 Discussion of the result of the reduction of a force system in space §5–6 Equilibrium equations of a force system in space and their applications §5–7 The center of a system of parallel forces and the center of gravity of an object Class of exercises

第五章空间力系 §5-1空间汇交力系 §5-2空间力偶系 §5-3力对点的矩与力对轴的矩 §54空间一般力系向一点的简化 四§5-5空间一般力系简化结果的讨论 四§5-6空间一般力系的平衡方程及应用 四§5-7平行力系的中心与物体的重心 习题课

6 第五章 空间力系 §5–1 空间汇交力系 §5–2 空间力偶系 §5–3 力对点的矩与力对轴的矩 §5–4 空间一般力系向一点的简化 §5–5 空间一般力系简化结果的讨论 §5–6 空间一般力系的平衡方程及应用 §5–7 平行力系的中心与物体的重心 习题课

Statics 85-1 Concurrent force system in space 1. The projection and decomposition of a force on the axes in space (1The representation of force in space: a force is given by its magnitude, its direction and its point(line)of application magnitude: F=F O y/point of application: the point at which the force acts onto the object direction: it can be determined by the three angles a B, y or by the angle of inclination 6 and the angle of depression p. a 7

7 §5-1 Concurrent force system in space 1. The projection and decomposition of a force on the axes in space: (1)The representation of force in space: a force is given by its magnitude, its direction and its point (line) of application magnitude: point of application: the point at which the force acts onto the object. direction: it can be determined by the three angles , , g or by the angle of inclination  and the angle of depression .  g  Fxy O F= F

学 §5-1空间汇交力系 一、力在空间轴上的投影与分解: 1.力在空间的表示: 力的三要素: 大小、方向、作用点(线) 大小:F=F 作用点:在物体的哪点就是哪点 2防向: 由a、B、y个方向角确定 由仰角θ与俯角q来确定

8 一、力在空间轴上的投影与分解： 1.力在空间的表示： 力的三要素： 大小、方向、作用点(线) 大小： 作用点：在物体的哪点就是哪点 方向： 由、、g三个方向角确定 由仰角 与俯角 来确定。  g  Fxy O F= F §5-1 空间汇交力系

Statics (2) The method of direct projection From the fig we see X=F cos a Y=FCOS B F Z=F·cosy (3) The method of indirect projection When the angles a, B and y are not easy to determine we can project F onto the plane xy firstly and then project the result f onto the axes x and y X-Fsin r cos=F. COS=.coSB- coso Y=FSiny.sin=Frv.sin=Fcose. sin z=F·cosy=Fsnb

9 (2) The method of direct projection From the fig we see g   cos cos , cos , =  =  =  Z F Y F X F X =Fsing cos =Fxy cos =Fcos cos Y =Fsing sin =Fxy sin =Fcos sin Z =Fcosg =Fsin (3) The method of indirect projection When the angles ,  and g are not easy to determine we can project F onto the plane xy firstly and then project the result Fxy onto the axes x and y

学 2、一次投影法(直接投影法) 由图可知:x=F:cosa Y=FCos R Z=F·cosy F 3、二次投影法(间接投影法) 当力与各轴正向夹角不易 确定时,可先将F投影到xy 面上,然后再投影到xy轴上, X=Fsin.cos=Frv. coS=F cosB.coS Y=FSiny sin=Fry sin=Fcose. sin Z=FcOSy=Fsin 10

10 2、一次投影法（直接投影法） 由图可知： g   cos cos , cos , =  =  =  Z F Y F X F X =Fsing cos =Fxy cos =Fcos cos Y =Fsing sin =Fxy sin =Fcos sin Z =Fcosg =Fsin 3、二次投影法（间接投影法） 当力与各轴正向夹角不易 确定时，可先将 F 投影到xy 面上，然后再投影到x、y轴上， 即