, .
( ):
. , , .
( M( F 1, F 2 ) ) :
M= Fd. | (1.10) |
.1.14
: , , - .
.1.14 (, ') (, ') : M 1 =Pd 1; M2=-Qd 2.
, , (.1.14).
, , , , .
.1.15
(.1.15). ( 1; 2), =F 1 × d= F 2 × d. 1 , .
0 ()= -F 1 × ;
0 ()= F 2 × (d+ a).
F 1 = F 2, :
0 ()+ 0 ()= - F 1 × + F 2 × (d+ a)= F 2 × d = ,
.. . :
0 ()+ 0 () = . | (1.11) |
( ). , .
, . [6]
1. ?
2. ?
3. ?
()
.1.16
0xy XY, .
, , 0xy (.16).
F XY = Fcosq, q - XY.
, , , (. .1.16):
FX= FXY cosj = Fcosq cosj; FY = FXY sinj = Fcosq sinj; FZ= Fsinq. | (1.12) |
0z.
|
|
- , (. ) , , (.).
.1.17
.
0() r ´ F. | (1.13) |
() :
ç 0()ç= M 0(F) = = F× h, | (1.14) |
F h, 0 . :
h = - - , 0 ;
- .
0() , .
:
( ) ( ), ; ( 0() ) .
0 0 , . , ( , 180) ( 0; . .1.17) , .
F h, 0 :
M0() = Fh | (1.15) |
- (ͷ).
.
0 (M 0() = 0), :
(F = 0);
- 0 ( h = 0).
.1.18
, F X, F Y, F Z x,y,z (.). 0 :
0() = =MX ()+MY () + MZ () , | (1.16) |
, , - 0x, 0y, 0z, 0() (.1.18) :
M X () = y F Z - z F Y, M Y () = z F X - x F Z, MZ () = x FY - y FX. | (1.17) |
: M X(), M Y(), M Z() 0x, 0y, 0z ( ).
M 0() :
M 0 () = . | (1.18) |
1. , ?
2. .
3. ?
.1.19
, , .
|
|
, 0x, 0y, 0z .
(.1.19).
, , :
, , .
, 0z:
M Z () = F XY× h | (1.19) |
, , , , .
, .19 0z | XY| 0xy h 0, : M Z () = + F XY× h.
(M Z () = 0), :
- ( , F XY = 0);
- ( , , : h = 0).
, : , .
1. ?
2. ?
3. h ?
.1.20
( M (F, F) ) - :
= . | (1.20) |
. , , , (.1.20), . , , , , . :
M = Fd, | (1.21) |
d - , , .
.
, , .