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T??M? V¤fxig"?￥
?
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x
f bW?￥8í ?iUS"fxig?￥Vr
T1
dV = pgdx1dx2dx3,(1.32)
￥Vr
T?gdxi?
"USMD7M?
^(1.32)
T ?
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S"?￥ü
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T.
8?Bc? w
H b ú￥f
}
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H b ú￥8íVr
T| x5.2?í[?
.
f
?1¨f
TK￥f
M
^B?2¨f
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TK?
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¨TK￥?s3V
U V¤
M = Mfifle(fi)?e(fl) = Mfifle(fi)?e(fl) = Mfifle(fi)?e(fl) = M flfi e(fi)?e(fl),(1.33)
? TK ?
s3￥Vr
T(1.26)
T, V[¤??tUSs
￥Vr
T1
Mfifl = TfiKfl; Mfifl = TfiKfl; Mfifl = TfiKfl; M flfi = TfiKfl,(1.34)
V
T V[ A?f
?
^?￥.
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2¨f
B?￥2¨f
ˉ V[¨(1.33)
T ?V
U.?ii?
^ ?B?2¨f
?
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￥
f
. ?T?B
? ?￥,(1.34)? ?iUS"?? ??
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?iUS"?A?
@
B?￥?é è ?μM11=M21 = M12=M22? ?.
2??
Mfifl1
@
I ù"￥?é?
?1B?2¨f
￥USs
;? (1.33)￥PHM
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, ?]￥US" úZ?·Hμ?]￥?.? USMD/￥MD
pX
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[2¨f
M￥ò?USs
USMD/￥MD
p???V
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fi0
@xfi
@xfl0
@xfl M
fifl;
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fi
@xfi0
@xfl
@xfl0 Mfifl;
Mfi0fl0 = @x
fi0
@xfi
@xfl
@xfl0 M
fi
fl; (1.35)
M fl0fi0 = @x
fi
@xfi0
@xfl0
@xfl M
fl
fi,
yN, V[| USMD/
@(1.35)
p￥2?Z? AT
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Mμ4FUSs
:
I
MUSs
Mfifl,xMUSs
Mfifl,MUSs
MfiflM flfi,
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V¨f
?é?·
S￥
6?,?"S??￥MD. è ?,Mfifl = gfi?gfl”M?”.]
H Q4?
IM·S1 ·
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M·S ·/?,?
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B /
H,
H1?i·S￥Q?,i
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f
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a
ü??
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ü
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a
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T ?
a
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:
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¨(1.22)ü
T?￥xM?MD?
IM? ?¨(1.12)é?
?
4¤?
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a
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^]B?f
￥?]USs
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@x
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@x?
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@x” T
fi0fl0
0?0”0,(1.36)
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USMD/￥MD
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T.
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T
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1.51y
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ds2 =?(1? !
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c2 )c
2dt2 +dr2 +r2d 2 +dz2 +2!r2
c cdtd ;
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o
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?dxi
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ids2
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fi
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fi0dxfl0 = gfi0fl0dxfi0dxfl0:
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USMD/￥MD
p
^
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fi
@xfi0
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?(1.9)μ???BB￥
IM?F. M bW
^
ü
°￥ bW,
^?9
ê4?BF??BB￥?;?B
? 8￥ M bW,s?
^ \?￥. V[|???BB￥
?F×?L?F7?1??BB?F. ?7,??
H
b￥? w,? V
s?B?dB￥MD,|
H b
μ?￥
M bW
=￥
IM?F?D???BB?F,?
? w
H b￥?
? 1MD?? V?
^]
"￥? ?.
[, ? w
H b?üè
￥
^???BB
￥?F.
m1.2A
U
H bUS" M bW
IM?-W￥1". 4?
H bM?ê4
US"(ct; xi),M??
M
u
US?
L,
H b?A),?￥ M bW
IM?e(o)e(i)D?)￥USLM M.
ì￥
vlZ_?gfifl %?,B??
^??BB￥.
??]￥US", M bWμ?]￥?.C ? A
IM?_
USMD/￥MD
p,(1.18)
T
PH
^DUS"ê4í1￥_
,·HTfi USMD/?(1.15)A
U￥
p MD,?
^ V??VUS
"fxfigMD?US"fxfi0g
H
IM?_
￥MD1"
^
e(fi0) = @x
fi
@xfi0e(fi) (1.21)
xM?A ?, M bW? ?BFL?? ?￥_
? V[¨ ? T?.C V
IM??¨
IM ?/
6BF?.
e(fi) = gfifle(fl),(1.22)
VxMgfifl
IMgfifl￥o
I1"(1.12) V[¤?
e(fi) = gfifle(fl),(1.23)
?¨
=
^L?
IM?￥
=1"(1.20)
T V¤
e(fi) ￠e(fl) = gfifl; e(fi) ￠e(fl) = –fifl (1.24)
T
a
üxM?￥éMo￥C??
IMgfifl ? %?9
a
ü
H bUS"ê?-a M bW
1 ?1μxM
IM2F?
ìMo-WμB?￥??.
6?Bc? w
H b ú￥f
}
1??|
￥??, h?iS
ü
^?+??￥S:(fi)xM?7y ·
?,
IM?
5 ·/?,i{μ ?|;7B?_
￥
IMUSs
￥·S ·
?,/
1o
￥xMUSs
￥·S ·/?, M
j.
¨(1.10),(1.21)(1.22)
T V[¤?xM? USMD/￥MD
p
e(fi0) = @x
fi0
@xfi e
(fi),(1.25)
xMUSs
?",f
T ê42??]￥?Faμ?]￥USs
:
IMUSs
xMU
Ss
, V1
T = Tfie(fi) = Tfie(fi),(1.26)
Tfi?1f
T￥xMUSs
.
?l
IM?xM?￥1"a, V[?
?USs
-W￥1":
Tfi = gfiflTfl; (1.27)
Tfi = gfiflTfl,(1.28)
??
f
IMUSs
xM
USMD￥MD
p(1.15)(1.10),V(1.27) V¤xMUS
s
USMD￥MD
p
Tfi0 = @x
fi
@xfi0 Tfi,(1.29)
9 ?
a,ó?￥? w
H b ê4
B?US"a,f
￥USs
9ü ??
,?
H
H b?
B?￥ M bW úμ2F?
IM?xM?.B? M_
?
F?
μ
FUSs
IM
xMUSs
.
ì-W￥1"?f
%?.f
'
&DUS"￥ê4í1,? USs
USM
D/SL?
QMD,?USMD￥ MMD(g'? V1 ?) %.
f
-W￥
f
-W￥}
μ f
-W￥FhE
f
-W￥eEf
·S
￥
6?f
·S￥
êif
.f
| /??o
.
n51?i? w
H b
ü°
H b￥B?×1μs ? w
H b??]?￥ M bWi?×,yN?
]?)￥ M_
??]￥ M bW. ?l8"üB??)￥ M_
M??
6B?￥ M bW- -,oμ
?]B M bW￥ M_
-W?
é?}
.
?f
MF-a ˉ ?
^B?f
. è ?S = K+T, USs
￥1"1
Sfi = Kfi +Tfi; Sfi = Kfi +Tfi:
?^￡SfiSfi USMD/sY
@(1.15)(1.29).
f
Me￥2T9
^f
. è ?M = cT,5μ
Mfi = cTfi; Mfi = cTfi:
?t5B?L? bW?_
￥
5
^? ?B"￥.
f
·S￥
6?¨ ?
L?, ?(1.27)(1.28)
U.
?f
W
=￥?l(1.16)C V?
T￠K = TfiKfi = TfiKfi,(1.30)
@?
￥±s+? us M bW? M bW, M_
? M_
.'
T1B'?? ?
ê￥? S
N
àμí[ us,7
^
<?? ??US"￥f
G ?US"ê4￥f
USs
W￥ uY.
x1.3S
ú¨f
7
T V A?
^f
·S￥
êi.?i·S￥
êi￥ù
^ B?xM·SB?
IM·S-Wé?￥,2?
IM·S2?xM·S-W
êi￥2TB??
^f
(?n'c 51.2).'
??|
IM·S ·
?,7xM·S ·/?.
Ka, h?ii?
^ ?B?μ4?s
￥
? V[ AT
^f
. è ?,USxfiü?
^B?f
,y1
USMDYè
^dL?￥,7f
￥USs
USMD/￥MD
^L?
QMD.L?V
üf
? M
bW, MD?USMD￥ MMDg'? V1 ? ? %?.
Q9V
üf
'
&DUS"￥ê4í1,B
?
,f
üVUSMDa ˉ
^
,f
.
1.3S
ú¨f
S
S
9?1
,¨f
.
^
H b?￥B?
′?G ??US"￥ê4. è ?,2?1¨f
￥
=(1.30)ü
^B?S
,y1?é?USMDfxfig!fxfi0g
H,μ
TfiKfi = @x
fi
@xfi0 T
fi0 @xfl
0
@xfi Kfl0 =
@xfl0
@xfi0 T
fi0Kfl0 = –fl0
fi0T
fi0Kfl0 = Tfi0Kfi0,(1.31)
Q4? ?·S B[?K C2Q.
aS
^B?
,
^· ó??￥ M bW7y￥. ?]￥
H b?,B?S
V[ |?]￥′,
??
H b
^B?S
f
.B???￥ è0
^Sò
·
U￥
HW.B?Sò￥ ?? ?
N?
4?
H b?￥BH wL,?1ò￥
W?L.
B
§W,òê?
W?L
￥B??.ò
￥
A ?
^ ??￥,
DUS"￥ê |í1,?
W?L
￥?]?,ò
￥
?].
[,ò
^
H b?￥B?S
f
,
W?L
μ?l.
t ?
L?ó4?￥2ToD?
￥`4??μ1,D 8￥US"ê4í1,
[BQ?
4??￥
??
^S
.1y
·? w
H b
ü°
H b?￥?
à
Qμv￥?]. '
a
￥c??11?W%1o
<lM
O?￥4?
?
.
x
f bW￥?M8í/
o
B?è¨￥S
bW￥8í.B?í kl￥ ?Z8￥8
^B?
DUS"í1￥+
[
^B?S
.5 ? A3?
x
f bWE3?￥8í. E3?9
^ V[ê4?B?
? ￥°?US"f?ig bW
^–ij, ?8í￥Vr
T
^d?1d?2d?3.
!fxig1B ?iUS"
1gijú?
D [???Xü? fxig"?￥8íVr
T1
dV = d?1d?2d?3 = jJjdx1dx2dx3;
? újJj
^Vf?ig"?fxig"USMD￥? V1 ?J = (@?i=@xj)￥?
T.
? V1 ?2?US"￥1" ?(1.11)
U.¨C ￥?|μ
G = JTEJ:
?GEsY?fxig"f?ig?￥xM.
T
H ?￥?
T??M? V¤fxig"?￥
?
Tg = jJj2.?"3?
x
f bW?￥8í ?iUS"fxig?￥Vr
T1
dV = pgdx1dx2dx3,(1.32)
￥Vr
T?gdxi?
"USMD7M?
^(1.32)
T ?
^B??M￥S
.o1??B?U
S"?￥ü
?US"?8í￥Vr
T.
8?Bc? w
H b ú￥f
}
à?<lM
?? w
H b ú￥8íVr
T| x5.2?í[?
.
f
?1¨f
TK￥f
M
^B?2¨f
,:?T?K=M.?f
TK?
^L?￥, è ?(aT+bQ)?K = a(T?K)+b(Q?K).
¨TK￥?s3V
U V¤
M = Mfifle(fi)?e(fl) = Mfifle(fi)?e(fl) = Mfifle(fi)?e(fl) = M flfi e(fi)?e(fl),(1.33)
? TK ?
s3￥Vr
T(1.26)
T, V[¤??tUSs
￥Vr
T1
Mfifl = TfiKfl; Mfifl = TfiKfl; Mfifl = TfiKfl; M flfi = TfiKfl,(1.34)
V
T V[ A?f
?
^?￥.
!K?T=?M,5?Mfifl = KfiTfl,B????Mfifl.
2¨f
B?￥2¨f
ˉ V[¨(1.33)
T ?V
U.?ii?
^ ?B?2¨f
?
^2?1¨f
￥
f
. ?T?B
? ?￥,(1.34)? ?iUS"?? ??
^?2¨f
?iUS"?A?
@
B?￥?é è ?μM11=M21 = M12=M22? ?.
2??
Mfifl1
@
I ù"￥?é?
?1B?2¨f
￥USs
;? (1.33)￥PHM
^B?? ?
?US"ê4￥f
, ?]￥US" úZ?·Hμ?]￥?.? USMD/￥MD
pX
?1.2?ó,
[2¨f
M￥ò?USs
USMD/￥MD
p???V
Mfi0fl0 = @x
fi0
@xfi
@xfl0
@xfl M
fifl;
Mfi0fl0 = @x
fi
@xfi0
@xfl
@xfl0 Mfifl;
Mfi0fl0 = @x
fi0
@xfi
@xfl
@xfl0 M
fi
fl; (1.35)
M fl0fi0 = @x
fi
@xfi0
@xfl0
@xfl M
fl
fi,
yN, V[| USMD/
@(1.35)
p￥2?Z? AT
^2¨f
￥USs
.V(1.33) Vn,?B?
ó?￥US",
IM?xM?F?2¨f
bW￥4??F,V71?2¨f
Mμ4FUSs
:
I
MUSs
Mfifl,xMUSs
Mfifl,MUSs
MfiflM flfi,
ì-W￥D
V¨f
?é?·
S￥
6?,?"S??￥MD. è ?,Mfifl = gfi?gfl”M?”.]
H Q4?
IM·S1 ·
?7x
M·S ·/?,?
·SB
B /
H,
H1?i·S￥Q?,i
=μA1￥ bì.
f
￥???M
?T
BUS"?2¨f
￥USs
@Mfifl = Mflfi,g'f
2?
IM·S?, ?^￡
ü???1" ?iUS"/?
@,7 ON
HMfifl 2?xM·S9
?(n 51.2).?
a
ü??
^?f
￥%μ?é.N
H??f
1?f
.f
ü
^B??f
.]"?Mfifl =?Mflfi
H??f
1Q?f
.?Q?f
,A ?μMfifi = Mfifi = 0 (? ú
×ˉ·Sfi? p).èH?f
^t ??Q?f
￥B?×1 è0. è? ?D [????è? <
H??? <
^]B?t ?
,
ì ?]￥US"?MoD.è? <H??? <
μ6?U
Ss
, B ?zF?B?2¨Q?f
x4.4 ú|í[W%￥)
.
6?,?i ?
BUS"?
μMfifl = Mflfi,???éB??
USMD/ ?,
[?
^f
￥%μ
?.
?^￡
ü2¨f
￥MUSs
F?￥ ?-,9ü
^ ?L
í
í-
^B?S
,?
U
SMD7M,7 OμMfifi = M fifi,?
^MfifiMfifi (? ú×ˉ·Sfi p)B??
^S
(?n 51.3).
x1.4?Bc 59
? s
a
ü·S￥
êi?? 1?
IM·S1?xM·S-Wé?.
f
￥Vr
T(1.8)?PH
^DUS"ê4í1￥S
·Hdxfi
^B?1¨f
￥
USs
[gfifl??
^B?2¨?f
￥USs
.V
USMD￥MD
p(1.10) ? A9
a
ü
^B?2¨f
￥xMUSs
. x1.1?¨(1.12)
T? ?
IMgfifl. V[¨(1.33)
T ?
a
ü
ì
^
]B?2¨f
?]?/￥?]USs
.
:
G = gfifle(fi)?e(fl):
¨(1.22)ü
T?￥xM?MD?
IM? ?¨(1.12)é?
?
4¤?
G = gfifle(fi)?e(fl) = –fifle(fi)?e(fl):
? s
a
ügfifl,gfifl–fifl
^]B?f
￥?]USs
.?i
￥MUSs
?US"??
^–f
,7 Of
^?￥,
[?A us
?MUSs
.
[
￡9 V[¨é?·S
6? ?é?.V -
￥D ??? a
M?¨é?USs
￥
·S
6??¨é?D
^Bí
Y.
ú¨f
¨? ?M]￥Z
T V[ a
M÷ú¨￥f
./
? B?5¨f
￥B?USs
US
MD/￥MD
T
Tfifl?” = @x
fi
@xfi0
@xfl
@xfl0
@x 0
@x
@x?0
@x?
@x”0
@x” T
fi0fl0
0?0”0,(1.36)
??
492 ?i¨f
￥USs
USMD/￥MD
p.
1.4?Bc 5
1.1V
IMxM￥o
I1"(1.12)
TxM USMD/￥MD
p(1.10)
T￡
ü
IM
gfifl USD/￥MD
p(1.13)
T.
1.2￡
ü2¨f
￥??( ?Tfifl = Tflfi)Q??( ?Tfifl =?Tflfi) USMD/ ??M
?Tfifl = TflfiB??
^USMD￥?M
.
1.3￡
ü2¨f
￥Tfifi = T fifi, O USMD/ ??M,?2¨xM
IMf
￥
Tfifi;TfifiB??
^USMD￥?M
.?
a
ü·S
êi
o
xM
IM·S-Wé?[
￡
êi￥2T
^f
.
1.4
!Afifl1?f
,Bfifl1Q?f
,
(a)￡
üAfiflBfifl=0;
(b)?Cfifl1 ?i2¨f
,:C(fifl) = 12(Cfifl +Cflfi),C[fifl] = 12(Cfifl?Cflfi),￡
ü?
T
CfiflAfifl = C(fifl)Afifl;
CfiflBfifl = C[fifl]Bfifl:
1.51y
"?￥1
ds2 =?(1? !
2r2
c2 )c
2dt2 +dr2 +r2d 2 +dz2 +2!r2
c cdtd ;
IMgfifl,ió
IM?xM?ò_
￥é#Mo
=.
? Is? g00 =?1; grr = 1; g0 = g 0 = !=c; g = 1=r2?!2=c2; gzz = 1, ?1
,.)
10?Bc? w
H b ú￥f
}
1.6
!2¨f
Tfifl
YVUSMD?, Oμ2?[
d
,￥?í
í,￡
ü?f
?
V1
?1¨f
￥f
,'Tfifl 6= Afi?Bfl, ?AfiBfl
^1¨f
.
1.7?
IM?xM?￥à
Q￡
ü/
Ti3
d cl.
efl(fi) = –flfi; e(fi)fl = gfifl; e(fi)fl = –fifl; e(fi)fl = gfifl,(1.37)
1.8:f
￥xMUSs
gfifl￥?
T1g.|gf
￥
IMUSs
gfifl A?
^gfifl￥f
, p￡
dg?” =?g?fig”fldgfifl; (1.38)
dg = ggfifldgfifl =?ggfifldgfifl,(1.39)
