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