, .
R*~{F1;F2;F3;;Fn} , ~{F1;F2;F3;;Fn -R*} . - .
. - , + -. - , .
(F)=Fh. + , , - .
=0, . (F)=Fh=2SDOAB
- r F. (F)=[r´F].
. ^ , r F , , .
½0(F)½= ½F½´ ½r½´sin(r; F); ½0(F)½= ½F½´ h=2SDOAB.
- , .. .
, ( ). R*=åFk.
, . , R*=0 ( .).
åFk=0 . åFk=0 åFkz=0
. - -: Fx=Fcosa, a- .
. 2 -: åFk=0; åFk=0 : F1, F2,, Fn, Î.
. 3- , , 3- . {F1;F2;F3 }~{R, F3}~0
n . n , n-1 , n- n-1 .
- . - -, ^ -.
z(F)=F h=2SDOAB
=0, ½½ . =0, .
z(F)=½0 (F)½cosa
- - .
SDOAB =SDOAB cosa.
. cos .
|
|
1/2 z(F)=1/2½0 (F)½cosaÞ z(F)=½0 (F)½cosa=½01 (F)½cosa1
0 (F)=[r´F]= i j k
x y z
Fx Fy Fz = (yFz zFy)i+(zFx-xFz)j+(xFy-yFx)k
x (F)= yFz zFy; My(F)=zFx-xFz; Mz=xFy-yFx.
z(F)=F h=2SDOAB
. - 2 -, .
F1=F1=F, d- . . ^- , , . . .
½1 (F1, F1)½=Fd=SðOABC. (F1)=[r1 F1]; (F1)=[r2 F1]= (F1)+ (F1)=[r1 F1]+[r2 F1]= [(r1- r2)F1]=[BO F1]; 1 (F1, F1) =[BO F1].
, .
, .
.
, , 2 , . , , , , . .
, .
, : å (F, F)=0.
, , . =1+2.
å (F, F)=0
å (F, F)=0
åz (F, F)=0 .
.
:
, .
F=F1=F1
(F1;F1)=Mo(F),
{F}~{F;F1;F1}~{Lo;F1}
(. ):
R , . R=åFk Lo=åMo(Fk)
. , .
R=0 Lo=0 - . - 6 -1 . :
åFk=0 åFk=0 åFkz=0 å(Fk)=0 å(Fk)=0 åz(Fk)=0 .
Î - , : åFk=0 åFk=0 å(Fk)=0 .
. ôô , åFk=0 å(Fk)=0
.
F1, F2, F3,,Fn ôô z, : åFkz=0 å(Fk)=0 å(Fk)=0
:
|
|
å(Fk)=0 å(Fk)=0 å(Fk)=0 ., ,, . Ï .
- :
, - . , å -=0, .. 3 .
- :
, - - . , , - , - , .. R*¹0 . . .
- 2-: , , R* . .. hR=0. . Ï R*=0, .. - .
- .
åFkz=0 å(Fk)=0 å(Fk)=0 .
- - , .. - , =0 .
- :
, - -, .. - R* R* ¹0 . , - 2 3 , R* .
- R*cosa=0, , R* 0, .. , - .
- - :
å(Fk)=0 å(Fk)=0, F1, F2, F3,,Fn
: - - , . - .
{F1,F2,, Fn}~R*, {F1,F2,, Fn, -R*}~0, å(Fk)= (R*)
. . . .
. . - , . . .: Lo^R.
:
1.. Lo=0; R¹0 , R*=R. R, . .
2. Lo¹0; R¹0. , . .
R=R1=R1; [Lo] ~{R1;R1}; {R1;R1}~0; , R R1 , , . {R1;R1}~0
{R;Lo}~ {R=R1=R1}~{R1}. D=Lo/R.
3. R=0, Lo¹0. . Lo. .. .
. . - . . . - ., - , .
- ., - . . - .
.
.
1.-F1cosa+XC=0
2.-XC+F2+XB=0
- F1cosa+ F2+XB=0
Rc=RC; MC=MC
: 6 - -, .
Q=[/], l=[]. Q=òqdx=qòdx=ql
Q(x)=(q/l)x, Q=òq(x)dx=(q/l)òxdx=(q/l)(x2/2)½= (ql)/2.
|
|
dQ=q(x)dx, [(ql)/2]b=òq(x) xdx=(q/l) ò x2dx=(q/l)(x3/3)½= (ql)/3.
[(ql)/2]b= (ql)/3Þb=(2/3)l.
: - .( . ).
. F..:
1) 0£ F£ F;
2) ,
3) . - -: F=fN, N- =, f--
4)- . - , , . .
. N=P. . .=dN, d-. . - -. -.
.
a R N, R- N .
tga= F/N=f-.
, R a - . R , - . .. - - , . R - , .
. - : d= ..=rQ, fP= F=Q
Q<(d/r)P (1), (2) -
1)Q<(d/r)P,d/r£f -
2) Q> (d/r)P, Q>fP ,
3) Q> (d/r)P, Q<fP
4) Q< (d/r)P, Q>fP
1, , , .
, - , - .
. . . . .
, - 0, . , 1.
Lo- {R, R}~0 R=R=R MO1=[O1O ´R] LO1=LO+[O1O ´R]= LO-[O1O ´R]
, . - - .
- -, - .
.. 1- - .
(LO1´R)=((LO+[O1O ´R])R)
(LO1´R)=(LO´R)+([O1O ´R] R)
(LO1´R)=(LO´R)
LO1´Cosa1= LO´ Cosa - .: .
L1xRx+ L1yRy+ L1zRz= LxRx+ LyRy+ LzRz
.
1)
LO¹0, R=0. .
2)
)R*=R; LO=0
, R, - - . . .
) LO¹0 R¹0, LO^ R.
, . .
|
|
R=R=R*
{R, LO}~{R=R=R*}~{R*}
LO=Rd
{R, R}~0
. , . d - R, -: d=Lo/R
3) . . . .
, .
LO¹0 R¹0, LO ^ R.
LO1=LOcosa;
LO2=LOsina; d=LO2/R
.
L1x/Rx= L1y/Ry= L1z/Rz-- . .
L1= L +[O1O ´R]
L1= L +[OO1 ´R]
[Lx+(y Rz -z Rx]/ Rx=[Ly+(z Rx -x Rz]/ Ry=[Lz+(x Ry -y Rx]/ Rz (- )
[Lx+(y Rz -z Ry]/ Rx=[Ly+(-x Rz +z Rx]/ Ry=[Lz+(x Ry -y Rx]/ Rz
i j k
x y z
Rx Ry Rz
[Lx -(y Rz -z Ry]/ Rx=[Ly -(z Rx -x Rz]/ Ry=[Lz -(x Ry -y Rx]/ Rz