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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) .





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