x, y, z xyz, , X, Y, Z XYZ (3.10), [ X ] [ x ]
, (3.14)
, (3.15)
, , - ; - , , OXYZ ( [ X ]) xyz ( [ x ] ), . . : [ X ] [ x 1] [ x 2][ x ], [ x 1] [ x 2] .
[ X ] [ x 1] ψ OY [ X ] (. 3.9 3.11).
[ x 1] [ x 2] θ [ x 1] (. 3.5 3.11, ).
. 3.9
[ x 2] [ x ] ( ) φ [ x 2] .
. 3.10
, XYZ ([ X ]) xyz ([ x ]), :
1. XYZ Y ψ, .. [ X ][ x 1], XYZ , (. 3.9 3.11, ). XYZ (. 3.11, a)
X = x 1 cos y + 0 + z 1 sin y,
Y = 0 + y 1 + 0,
Z = - x 1 sin y + 0 + z 1 cos y,
[ X ] ={a2y} [ x 1], (3.16)
{a2y} = (3.17)
Y ψ.
. 3.11
2. - θ, .. [ x 1] [ x 2],
, = (. 3.7,3.9, 3.11, ).
, . 3.11, , :
x 1 = x 2 cos q - y 2 sin q + 0,
y 1 = x 2 sin q + y 2 cos q + 0,
z 1 = 0 + 0 + z 2,
[ x 1] = {a3q } [ x 2], (3.18)
{a3q } = (3.19)
0z 1 q.
3. ( ) φ,..[ x 2][ x ](. 3.7, 3.9 3.11, ), Cxyz, , . 3.11, ,
x (2) = x cos j + 0 + z sin j,
y (2) = 0 + y + 0,
z (2) = - x sin j + 0 + z cos j,
[ x 2 ] = { a2j } [ x ], (3.20)
{ a2j } (3.17) {a2y} :
{a2φ} = . (3.21)
(3.16) (3.18), ,
|
|
[ X ] ={a2y} {a3q} [ x (2)], (3.22)
{a2y,3q } ,
{ a2y,3q } = { a2y} {a3q } =
= = (3.23)
= .
(3.16) (3.18) (3.20):
[ X ] ={a2y} {a3q} {a2j } [ x ]. (3.24)
(3.15) (3.24), , (3.17), (3.19), (3.21):
{ay,q,j } = = { a2y} { a3q } { a2j } =
= =(3.25)
(3.15) (3.25) .