, . , . , .
. , . . , .. , () , (. 3.1).
. 3.1
CXYZ, Cxyz (. 3.1). , CZ , CY ( ). Cxyz, , CXYZ : , , (. 3.2).
. 3.2
. 3.2, CXY Cxy , CX Cx. CYZ Cy Cy 1, Cy. CXYZ Cxyz, .
CXYZ Cxyz :
1) CXYZ CZ , Cx 1 y 1 z 1, Cz 1= CZ (. 3.3);
. 3.3
2) , , (. 3.4);
. 3.4
3) (. 3.5), Cxyz.
. 3.5
:
1) CXYZ (. 3.3)
X = x 1 cos y - y 1 sin y + 0,
Y = x 1 sin y + y1 cos y + 0, (3.1)
Z = 0 + 0 + z1 ,
:
[ X ] ={ a3y} [ x 1], , (3.2)
- , , CXYZ Z y,
; (3.3)
2) (. 3.4)
x 1 = x 2 + 0 + 0,
y 1 = 0 + y 2 - z 2 , (3.4)
z 1 = 0 + y 2 + z 2 ,
[ x 1] = [ x 2], , (3.5)
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, , , = ,
; (3.6)
3) Cxyz (. 3.5)
x 2 = x cos j + 0 + z sin j,
y 2 = 0 + y + 0, (3.7)
z 2 = - x sin j + 0 + z cos j,
[ x 2]= [ x ],
. (3.8)
{a2j } , { a2j }, Cxyz j = ,
. (3.9)
x, y, z , , X, Y, Z ,
, (3.10)
, (3.11)
: , , .
, CXYZ Cxyz, . , x, y, z X, Y, Z.
(3.2) (3.5) (3.8), :
. (3.12)
(3.11) (3.12), ,
=
=
.(3.13)
(3.2) (3.5), , , [ X ] = [ x 2]. = :
=
= (3.13 a)
, , (, , , ), : y (t), q (t) ( ) j (t). .
, . XYZ, , xyz, (. 3.6 3.8). , O, , xyz XYZ, , .. xyz
(. 3.5 3.8).
. 3.6
. 3.7
XZ ( ) xz ( ) (. 3.8) z (1) = z (2) = OE, y Z, j z, . , xz XZ q, Y y.
. 3.8
Y, y, .
q z 1 = z 2 = OE, .
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, ( )j Oy = Oy 2, ( ) .
3.6 3.8 , .. , OY, OE Oy.
xyz XYZ, .. : , ( ) .