《理论力学》课程教学资源（PPT课件，英文）Chapter 05 Space mechanics

THEORYMECHANICS1902Electronic teaching planChapter 5 Space mechanicsCollege of Mechanical andVehicle Engineering王晓君

THEORY MECHANICS Chapter 5 Space mechanics Electronic teaching plan College of Mechanical and Vehicle Engineering 王晓君

Spatial concurrent force systemMoment of force on axis andmoment offorce on pointSpace couple systemSimplification of the space forcesystemEquilibrium conditions andequations of the space force systemThe object's center of gravity

• Spatial concurrent force system • Moment of force on axis and moment of force on point • Space couple system • Simplification of the space force system • Equilibrium conditions and equations of the space force system • The object’s center of gravity

If the lines of action ofBY.each force inthe forcesystem are arbitrarilydistributed in space,the force system is(a)called spatial arbitraryZforcesystem,2Babbreviated as spatial5force system.(b)

If the lines of action of each force in the force system are arbitrarily distributed in space, the force system is called spatial arbitrary force system, abbreviated as spatial force system

The main content of this chapterSpace couple systemSpace force decompositionsystemSpatial concurrent force systenSimply Derive the equilibrium equationApplication:center of gravitycenter of parallelforce system

The main content of this chapter Space force system Spatial concurrent force system Space couple system Simply Derive the equilibrium equation decomposition Application: center of gravity, center of parallel force system

5.1 Spatial concurrent force systemIs the force polygon rule synthesized by planarconcurrent force system applicable to space concurrentforce system?R(a)(b)Is it easy to use multiple concurrent forces inspace?What about the analytical method?

Is the force polygon rule synthesized by planar concurrent force system applicable to space concurrent force system? Is it easy to use multiple concurrent forces in space? What about the analytical method? 5.1 Spatial concurrent force system

5.1 Spatial concurrent force system一, Decomposition and projection ofIzspatial force along coordinate axisFB1, Decomposition of force alongZFrectangular coordinate axisFAyIf a straight parallelepiped is made主with force vector F as diagonal and itsxxthree edges are parallel to thecan becoordinate axis, the force Fthreedirectlydecomposedintotheorthogonal componentsalongcoordinate axis

一、Decomposition and projection of spatial force along coordinate axis x y z A B F  Fx  Fy z  F  1、Decomposition of force along rectangular coordinate axis If a straight parallelepiped is made with force vector as diagonal and its three edges are parallel to the coordinate axis, the force can be directly decomposed into three orthogonal components along the coordinate axis. F  F  5.1 Spatial concurrent force system

5.1 Spatial concurrent force system2 Projection of force on rectangular coordinate axiszDirect projection methodF. = F cos ΦFF.=Fcos0一JF. = F cosy

Fx = F co s  2、Projection of force on rectangular coordinate axis Direct projection method 5.1 Spatial concurrent force system

5.1Spatialconcurrent force systemIndirect (secondary) projection methodF... = F sin yXF. = F sin ycospF.=FsinysinF, = F cos

Indirect (secondary) projection method 5.1 Spatial concurrent force system

5.1 Spatial concurrent force systemOn the contrary, if the projections X , Y and Z ofthe force F on the coordinate axis are known, themagnitude and direction of the force are:F = X?+y?+z?ZXY,cos B福=一,cOScosα =FFFAnalytical expression of force F :F=F.+F.+F.= Xi +Yi+Zk

On the contrary, if the projections , and of the force on the coordinate axis are known, the magnitude and direction of the force are: F  X Y Z 2 2 2 F = X +Y + Z F Z F Y F X cos = ,cos  = ,cos = Analytical expression of force : F  F F F F Xi Yj Zk x y z        = + + = + + 5.1 Spatial concurrent force system

5.1 Spatial concurrent force system二, Resultant and equilibrium of spatial concurrent force systemR=F+F+...+F, =ZF1、 Resultant resultant force:magnified: R= V(ZX) +(ZY)? +(ZZ)?ZXZZZYCOsdirection:cosα COSTRRR2、EquilibriumThe necessary and sufficient conditions fortheR=ZF=0equilibrium of spatial concurrent force system are:Expressed analytically as: Z X = O. ZY = O, Z Z = 0It's the equilibrium equation of the space force system

二、Resultant and equilibrium of spatial concurrent force system 1、Resultant R F F Fn F      = 1 + 2 ++ =  2 2 2 R = ( X ) + (Y) + ( Z) R Z R Y R X  =  =  cos = ,cos  ,cos 2、Equilibrium The necessary and sufficient conditions for the equilibrium of spatial concurrent force system are: R =  F = 0   Expressed analytically as：  X = 0,Y = 0, Z = 0 It’s the equilibrium equation of the space force system. resultant force： magnified： direction： 5.1 Spatial concurrent force system