Metody przemieszczeń (ciąg dalszy)

4
/'
,'#( -'2 -./ 0*&
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!"
#" $
$ $
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*.2"!3.#(%D A .*9494#B9
.*9494 3(.&1'- 7&1'-7 *.2"!3.#(%"/ 8 'B #'1. 7&1'-H :B #(FGE *.2"!3.#(%' 7&1'-7H
#B #(FGE '%!.*.2"!3.#(%' 7&1'-7
(0 D('% " 2"! -D ,3("2 "*(#(") , 0.C*("/ #'1"/ 7&1'-7 0 D('1 :. * F (
0.(%'#("% "2 I % "0 '- 2.#$ A .*949<B *("G# 7 &D!J0 :3 !78 ϕ4 ϕ < ϕ ?
ϕ K ϕ L ϕ M 3'( !3("#$ ,3("*70J08 δ < δ K δ L 9
.*949< #$"2'! , -*!'0 0. 3 (,'!3.0'%"/ #'1"/ 7&1'-7
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@ - ' #(FG# *.2"!3.#(%"6
@ - ' #(FG# '%!.*.2"!3.#(@
%"6
ϕ4 = −ϕ M
ϕ < = −ϕ L
ϕ ? = −ϕ K
δ < = −δ L
δK = =
ϕ4 = ϕ M
ϕ< = ϕL
ϕ? = ϕ K
δ< = δL
δK =
A494B
"'*7276D# - ' #(FG# *.2"!3.#(%"6 ( I % "0 '- 2.#$ , ( *!'1 K A0'3!
(03J# E 70'/F %' 5'&! C"8 δ K = = # 0.% &' (" (% *("% ' * F :# DC")B ('G - '
'%!.*.2"!3.#(%"6 L9
' , -*!'0 " , 0.C*(.#$ 0( 3J0 A494B 3'( 0#("G% "6*(.#$ 3.*7%&J0
A .*9494 : #B 2 C"2. ,3(",3 0'-( E %'*!F,76D#D /" 2"!3.#(%D 3"-7&#6F 7&1'@
-J08
.*949? 3"-7& 0'%" #(FG# 7&1'-78 'B *.2"!3.#(%'H :B '%!.*.2"!3.#(%'
",3(.,'-& 0 ('*! * 0'% 0 , 0.C*(.#$ 7&1'-'#$ A .*949?B !'& " ' % "
%%" , -,'3# ' A('2 # 0'% "B ,3F!J0 G3 -& 0.#$9
& %'% !"/ %' , -*!'@
0 " '%' (. ,3("2 "*(#(") 3 (,'!3.0'%.#$ 7&1'-J08
'B 0 7&1'-( " *.2"!3.#(%.2 ('*! * 0'% , -, 3F G (/ 0D /-.C 0.*!D, D %'@
*!F,76D#" ,3("2 "*(#("% ' ,3F!'8
ϕ = = → &D! :3 !7 , 0*!'1. ( "0"6 *!3 %. ,3F!' 3J0%. 6"*! &D! 0 ( ,3'0"6
'"
( ,3("# 0%.2 (%'& "2 0 F# * F 3J0% 0'CDH
= = → 0*(.*!& " * 1. , ( 2" -( '1'6D#" %' ,3F! 3J0% 0'CD * F A, 2 6'2
*&3J#"% " ,3F!'BH
!"#$% &'
(%')*&'+
,'#(
-./ 0*&
'01 0*&
1 !& 0 '&
.2,"3
?
≠ = → :3'& 3J0% 0'/ * 1 , % 0.#$H
:B 0 7&1'-( " '%!.*.2"!3.#(%.2 ('*! * 0'% , -, 3F ,3("/7: 0 @,3("*70%D
/-.C 0.*!D, D %'*!F,76D#" ,3("2 "*(#("% ' ,3F!'8
ϕ ≠ = → :3'& 3J0% 0'/ &D!J0 :3 !7H
≠ = → :3'& 3J0% 0'/ * 1 , ( 2.#$H
= = → 0*(.*!& " * 1. , % 0" -( '1'6D#" %' ,3F! 3J0% 0'CD * FH
%' / #(%D '%' (F :F-( "2. ,3(",3 0'-('E 3J0% "C - ' %%.#$ 7&1'-J09
,3(.&1'-7 , % C"6 ,3("-*!'0 % & &' ( % #$ A .*949K .*949LB9
'
.*949K 3(.&1'- 7&1'-7 *.2"!3.#(%"/ ( ,3F!"2 0 * *.2"!3 8 'B #'1. 7&1'-H :B #(FGE
*.2"!3.#(%' 7&1'-7H #B #(FGE '%!.*.2"!3.#(%' 7&1'-7H -B (3"-7& 0'%' #(FGE *.2"@
!3.#(%'H "B (3"-7& 0'%' #(FGE '%!.*.2"!3.#(%'
!"#$% &'
(%')*&'+
,'#(
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'01 0*&
1 !& 0 '&
.2,"3
K
.*949L 3(.&1'- 7&1'-7 *.2"!3.#(%"/ ( ,3("/7:"2 0 * *.2"!3 8 'B #'1. 7&1'-H :B
#(FGE *.2"!3.#(%' 7&1'-7H #B #(FGE '%!.*.2"!3.#(%' 7&1'-7H -B (3"-7& 0'%' #(FGE
*.2"!3.#(%'H "B (3"-7& 0'%' #(FGE '%!.*.2"!3.#(%'
%"
$
&
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(2 '%D *(!.0% G# 0 ,3F# " A%,9 & %*!37&#6' , - *70% #FB9
!'& 2 ,3(.,'-&7
2 C"2. ('*! * 0'E %'*!F,76D#" *, * :. , *!F, 0'% '8
'B 70(/ F-% E (2 "%%D *(!.0% G# ,3F!' 0" 0( 3'#$ !3'%*5 32'#.6%.#$
.*9<94 3F! (2 "%%"6 *(!.0% G# 8 'B 0.27*( %" 7 /J % %" ,3("2 "*(#("% '
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%"6 0 2 "6*#'#$ % "0 '- 2.#$
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α + β =4
<
=γ ⋅
4
.,3 0'-("% "8
4 4
4  4
4 
<
<
 < ⋅ α ⋅ ⋅ 4 ⋅  ? ⋅ 4 + ? ⋅ β  + < ⋅ α ⋅ ⋅ β ⋅  ? ⋅ β + ? ⋅ 4 +




4 

4 4
< 
β? 
?


4
+
⋅
⋅
⋅
⋅
⋅
=
=
−
+
β
β
β
β

γ 
? 
? ⋅ 4 
4γ  <
δ 44 =
!"#$% &'
(%')*&'+
,'#(
-./ 0*&
'01 0*&
1 !& 0 '&
.2,"3
M
δ << =
+
4 4
4 
<
⋅ β ⋅ ⋅ α ⋅  ⋅ α + ⋅ 4  +

? 
?
4γ  <
4 4
< 
 < ⋅ α ⋅ ⋅ α ⋅ ? ⋅ α  +
4
4 4
4 
<
⋅ β ⋅ ⋅ 4 ⋅  ⋅ 4 + ⋅ α  =

? 
?
4γ  <
=
?⋅
4 4
4
4
< 
 < ⋅ α ⋅ ⋅ 4 ⋅ ? ⋅ α + < ⋅ α ⋅ ⋅ β ⋅ ? ⋅ α  −
4
δ 4< = δ <4 = −
4 4
4 
<
⋅ β ⋅ ⋅ β ⋅  ⋅ α + ⋅ 4  =

? 
?
4γ  <
−
=−

α? 
4 + α ? −

γ 
4 
=
 <
< β <α + β < 
α + <α < β +

γ

4 
M⋅
4
∆4∆ = −4 ⋅ ϕ − ⋅
+
4
=
= −ϕ + Ψ
4
∆ < ∆ = −4 ⋅ ϕ − ⋅
+
4
=
= −ϕ + Ψ
, -*!'0 "% 7 - 7&1'-7 3J0%')8
δ 44 4 + δ 4<

δ <4 4 + δ <<
<
+ ∆4∆ = =
<
+ ∆ <∆ = =
!3(.2'2. %'*!F,76D#" 0.% & 8
ϕ −Ψ +
4
=
=
=
?
<
=
=
<

α?  
β?  4  <
< β <α + β <  
 − α + <α < β +
 
4 + α ? −  ⋅ 4 − β ? +
γ  
γ  K
γ

 
4 
4
(ϕ − Ψ
<
=
?
!"#$% &'
<
<


4
(ϕ − Ψ )⋅ α < + <α < β + < β α + β 
γ
<


4
) + (ϕ
−Ψ



γ 
)⋅ 4 + α ? − α

A<94B
?
<

< β <α + β <  
α?  
β?  4 <
 ⋅ 4 − β ? +
 − α + <α < β +
 
4 + α ? −
γ  
γ  K
γ

 
(%')*&'+
,'#(
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N
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*!'0 "% " -'%.#$ :. 7(.*&'E 0( 3. 6'& - ' ,3F!'
*!'1"6 *(!.0% G# A!(%9
α = 4 β = = γ = 4 7: α = = β = 4 γ = 4 B9
4
=
=
=
<
=
=
=
<⋅
4
⋅ (<ϕ + ϕ − ?Ψ
)
<⋅
4
⋅ (<ϕ + ϕ − ?Ψ
)
A<9<B
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A .*9L94'B9
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4
<
4 4 4
⋅ ⋅4 ⋅ ⋅ ⋅4 + ⋅ ⋅ =
<
?
Κ ?
= −4 ⋅ ϕ = −ϕ
δ 44 =
∆4∆
4
+
<
4
⋅Κ
, -*!'0 "% 7 - 3J0%'% '8
δ 44 4 + ∆4∆ = =
!"#$% &'
(%')*&'+
,'#(
-./ 0*&
'01 0*&
1 !& 0 '&
.2,"3
44
!3(.2'2. %'*!F,76D#. 0.% &8
 ? ⋅ < ⋅Κ 
−ϕ
ϕ
∆
 =
= − 4∆ = −
= ?
= ϕ  ?
4 =
4
?
?
⋅
Κ
+
⋅
Κ
+
δ 44


+ <
?
⋅Κ
? ⋅ < ⋅Κ
AL94B







?
?
?
4  ?
⋅Κ
⋅Κ
 = ?  κ ϕ
=
=
⋅
ϕ ?
ϕ
?
  ⋅Κ


 ⋅Κ + ?
 ?+κ 



+ ?  



 
 
/-( "8
κ=
Κ⋅
?
0"3.5 &762. , ,3'0% GE 7(.*&'%"/ 3 (0 D('% ' A0(J3 L94B ,3("( !'& " , -@
*!'0 "% " -'%.#$ :.8
@ 7(.*&'E 0(J3 - ' :" & % ", -'!%"6 , -, 3(" A% "*& )#("% " *(!.0%"6B #(.
('2 "% '2. *,3FC.%&F %' ,3F! ' 0!"-. - ' , -, 3. ,3("/7: 0 ,3("*70%"68
Κ = ∞ →κ = ∞
κ
κ
κ
2
= 2
=4
κ →∞ κ + ?
κ →∞ κ
+?
κ
κ
*!D-8
4
=
=
?
ϕ
AL9<'B
0.C"6 !3(.2'%. 0.% & A0(J3 L9<'B 6"*! (/ -%. ( (%'%.2 %'2 0( 3'2
!3'%*5 32'#.6%.2 9
@ 7(.*&'E 0(J3 - ' :" & % "*(!.0%"6 , -, 3(" A% "*& )#("% " , -'!%"6B #(.
" 2 %76"2. , -,'3# " *,3FC.%&D ' 0!"-. - ' *0 : -%"/ & )#'8
Κ = = →κ = =
*!D-8
=
==
AL9<:B
0.C"6 !3(.2'%. 0.% & A0(J3 L9<:B 6"*! (/ -%. ( %'*(.2 ,3("0 -.0'% '2
/-.C 6"*! 7&1'- *!'!.#(% " 0.(%'#(' %.9
4
:B ,3(. 0.& 3(.*!'% 7 0( 3J0 !3'%*5 32'#.6%.#$
!"#$% &'
(%')*&'+
,'#(
-./ 0*&
'01 0*&
1 !& 0 '&
.2,"3
4<
& 3(.*!'2. !7!'6 ('*'-. *7,"3, (.#6 *&7!&J0 A!(%9 ( ('*'-. /1 *(D#"6 C"
*!'!"#(%. *&7!"& -( '1'% ' & &7 ,3(.#(.% 6"*! 3J0%. *72 " "5"&!J0 -( '1'% '
&'C-"6 ( ,3(.#(.% ( * :%'B *!D-8
= S + SS
AL9?B
/-( "8
S
@ ,3(F*1 0. ,3(.0F(1 0. 2 2"%! (/ %'6D#. - ' , -, 3. % ",3("*70%"6
SS
@ ,3(F*1 0. ,3(.0F(1 0. 2 2"%! (/ %'6D#. - ' , -, 3. *,3FC.*!"6
" & GE
S
: #(.2. 0,3 *! (" 0( 3J0 !3'%*5 32'#.6%.#$8
=
S
" & GE
SS
?
ϕ
AL9KB
: #( %' (" 0( 3J0 !3'%*5 32'#.6%.#$ ,3(.62 " , *!'E8
SS
=
−?
Ψ
AL9LB
.*9L9< 3("-*!'0 "% " 7 /J % %.#$ 0.27*( %.#$ ,3("2 "*(#(") , -,J3 0F(1 0.#$
0 3 (,'!3.0'%"6 :" #"
D! Ψ 6"*! 3J0%. A .*9 L9<B8
Ψ =
" 0( 3J0
∆
AL9MB
%& "3' - ' *,3FC.%. % 0"6 2 C"2. (', *'E C"8
∆ =
AL9NB
Κ
!D- %' , -*!'0 " , 0.C*(.#$ 0( 3J0 AL9M L9NB 2 C"2. (', *'E8
SS
"'&#6"
=
−?
Ψ =
SS
!"#$% &'
⋅
∆
=
−?
⋅
AL9OB
Κ⋅
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=
ϕ
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? 
 Κ⋅ 
Κ⋅ ? +?  ?

 =
ϕ
?
 Κ⋅

=
=
?
?
 Κ⋅ ?
ϕ 
?
Κ⋅ +?
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<
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4
⋅ ⋅4 + ⋅ ⋅ =
+ <
?
Κ ?
⋅Κ
<
4 4 4
4
⋅ ⋅4 + ⋅ ⋅ =
+ <
?
Κ ?
⋅Κ
4
4
4 4 4
⋅ ⋅4 ⋅ ⋅ ⋅4 + ⋅ ⋅ = −
+
<
?
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Κ
∆4∆ = −4 ⋅ ϕ = −ϕ
∆ <∆ = =
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=
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K
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
 =

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 =

=
=
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
ϕ
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K
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κ +?
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κ
κ
κ =4
= 2
=4 2
= 2 κ
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+
+
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κ
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Κ = = →κ = =
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=
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<
=
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⋅ ⋅4 ⋅
<
4
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δ 44 =
4
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<
⋅ ⋅4 =
?
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<
4
4
⋅ ⋅4 + 4 ⋅4 ⋅ =
+
?
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4
4
4
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<
?
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δ 44 4 + δ 4<

δ <4 4 + δ <<
<
+ ∆4∆ = =
<
+ ∆ <∆ = =
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=
<
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⋅χ
ϕ 
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=
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ϕ
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ϕ
κ
+
K
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κS =
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χ = ∞ →κS = ∞
κS S + ? S
κS S
S
κS +?
κ
κ =4 2
2 S
= S 2 Sκ
= S2 S κ
=4
S
κ S →∞ κ + K
κ →∞ κ
κ S →∞ κ + K
κ →∞ κ
K
K S
S +
S
S +
κ
κ
κ
κ
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=
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ϕ
<
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χ = ∞ →κS = ∞
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=
=
?
ϕ
<
=
==
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