《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

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