ISSN 1561-9087 à¨ª« ¤­  £÷¤à®¬¥å ­÷ª . 2000. ’®¬ 2 (74), N 3. ‘. 65{74
“„Š 532.528
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In
uence of a supercavitating model design parameters on the model range and its perturbed motion features is investi-
gated. It is shown, that a propulsive devise can increase the model range if high-ecient fuel were used only. The model
perturbed motion depends on clearance between the model stern part and a cavity wall. If clearance is grate, the motion
is stationary oscillation, amplitude and frequency being independent on initial conditions. Dierent forms of motion are
possible if clearance is small: unstable motion, stationary asymmetric oscillation, irregular oscillation.
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ISSN 1561-9087 à¨ª« ¤­  £÷¤à®¬¥å ­÷ª . 2000. ’®¬ 2 (74), N 3. ‘. 65{74
á⥭ª ¬¨ ª ¢¥à­ë. ®áª®«ìªã ¢â®à®© ¨ âà¥â¨©
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66 ‘. ˆ. ã⨫¨­
ISSN 1561-9087 à¨ª« ¤­  £÷¤à®¬¥å ­÷ª . 2000. ’®¬ 2 (74), N 3. ‘. 65{74
150¬¬ á ª ¢¨â â®à®¬¤¨ ¬¥â஬1 ¬¬¨¬¥¥â ¤ «ì-
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= 
b
W
c
(10)
¢ ª®­æ¥ ¯ãâ¨.
‚ १ã«ìâ â¥ ®¡é¨© à á¯®« £ ¥¬ë© ¨¬¯ã«ìá á®-
áâ ¢¨â
K
0
= m
0
V
0
+W
c
[
f
Q
f
BnZrV
0
(
b
BnZr
f
)]: (11)
¨á. 2. ‘奬  ¬®¤¥«¨
‚ëà ¦¥­¨¥ ¢ ᪮¡ª å ®¡à é ¥âáï ¢ 0 ¯à¨
V
cr
= Q
f

f

b
BnZr
f
: (12)
à¨ V
0
<V
cr
, ­ ç «ì­ë© ¨¬¯ã«ìá 㢥«¨ç¨¢ ¥â-
áï, ¨ ¬®¦­® à ááç¨â뢠âì ­  㢥«¨ç¥­¨¥ ¤ «ì­®-
áâ¨.  ¯à®â¨¢, ¯à¨ V
0
> V
cr
®­ 㬥­ìè ¥âáï, ¨
á«¥¤ã¥â ®¦¨¤ âì, çâ® ¬®¤¥«ìá ¤¢¨£ â¥«¥¬ ¯à®©¤¥â
¬¥­ì襥 à ááâ®ï­¨¥, 祬 ᯫ®è­ ï.
„«ï à áç¥â  ¤¢¨¦¥­¨ï ¬®¤¥«¨ á ¤¢¨£ â¥«¥¬ ¡ë-
«  ࠧࠡ®â ­  ¯à®£à ¬¬  CDILM, ¢ª«îç îé ï
¡«®ª ¤«ï à áç¥â  å à ªâ¥à¨á⨪ ⥫  á ¯®«®áâìî,
§ ¯®«­¥­­®© ⮯«¨¢®¬, ¨ ¡«®ª ¤«ï à áç¥â  â
¤¢¨£ â¥«ï; ãà ¢­¥­¨ï ¤¢¨¦¥­¨ï ¤®¯®«­¥­ë á®®â-
¢¥âáâ¢ãî騬¨ á« £ ¥¬ë¬¨.
‚ ¡«®ª¥ à áç¥â  å à ªâ¥à¨á⨪ ⥫  ¯à®£à ¬¬ë
CDILM ¢­¥è­¨© ª®­âãà ⥫   ¯¯à®ªá¨¬¨àã¥âáï
ç¥âëàì¬ï ãá¥ç¥­­ë¬¨ ª®­ãá ¬¨ (à¨á. 2). Œ®¤¥«ì
¬®¦¥â ᮤ¥à¦ âì ¯®«®áâì ¢ ¢¨¤¥ ãá¥ç¥­­®£® ª®-
­ãá , ­ ç¨­ î饣®áï ­  § ¤ ­­®¬ à ááâ®ï­¨¨ ®â
ª ¢¨â â®à  ¨ § ª ­ç¨¢ î饣®áï ¢ ª®à¬¥ ¬®¤¥«¨.
Ž¯à¥¤¥«ïîâáï: ®¡ê¥¬ ¬®¤¥«¨ ¯® ¥¥ ¢­¥è­¥¬ã ª®­-
âãàã, ®¡ê¥¬ ¯®«®áâ¨, ¬ áá  ¬®¤¥«¨ á ⮯«¨¢®¬,
¬ áá  â®¯«¨¢ , ¯®«®¦¥­¨¥ 業âà  ¨­¥à樨 ¨ ¬®-
¬¥­â ¨­¥à樨.
«®ª à áç¥â  â ¢ë¯®«­ï¥â à áç¥â ¬ ááë ⮯-
«¨¢ ¨ ¥¥ ¯à®¨§¢®¤­®©¯® ¢à¥¬¥­¨. à¨ í⮬ ¯à¥¤-
¯®« £ ¥âáï, çâ® £®à¥­¨¥ ­ ç¨­ ¥âáï ¢ ¬®¬¥­â ¢à¥-
¬¥­¨ t
0f
,   ᪮à®áâì £®à¥­¨ï ï¥âáï «¨­¥©­®©
ä㭪樥© ¢à¥¬¥­¨. “à ¢­¥­¨¥ ¤«ï à áç¥â  ¬ ááë
­¥á£®à¥¢è¥£® ⮯«¨¢  ¨¬¥¥â ¢¨¤
m
f
(t) = m
f0

1BnZra
f0
(tBnZrt
0f
)BnZr
1
2
a
f1
(tBnZrt
0f
)
2

:
(13)
‘«¥¤®¢ â¥«ì­®,
‘. ˆ. ã⨫¨­ 67
ISSN 1561-9087 à¨ª« ¤­  £÷¤à®¬¥å ­÷ª . 2000. ’®¬ 2 (74), N 3. ‘. 65{74
¨á. 3. ‚«¨ï­¨¥ íä䥪⨢­®á⨠⮯«¨¢  ­  ¤ «ì­®áâì
T
p
(t) = Q
f
m
f0
[a
f0
+a
f1
(tBnZrt
0f
)]: (14)
‡¤¥áì m
f0
{ ­ ç «ì­ ï ¬ áá  â®¯«¨¢ . Š®íä-
ä¨æ¨¥­âë a
f0
[á
BnZr1
] ¨ a
f1
[á
BnZr2
] ®¯à¥¤¥«ïîâ ᪮à®áâì
£®à¥­¨ï ⮯«¨¢ .
‚ ¯à®æ¥áᥠáç¥â  ¢ë¢®¤ïâáï ¯à®©¤¥­­ë© ¯ãâì,
᪮à®áâì, ¢à¥¬ï, â ¨ ®áâ â®ª ⮯«¨¢ . ‘ç¥â
¯à¥ªà é ¥âáï, ¥á«¨ ᪮à®áâì ¨«¨ ª¨­¥â¨ç¥áª ï
í­¥à£¨ï 㬥­ìè «¨áì ¤® § ¤ ­­®© (ªà¨â¨ç¥áª®©)
¢¥«¨ç¨­ë, § §®à ¬¥¦¤ã ⥫®¬ ¨ ª ¢¥à­®© 㬥­ì-
è «áï ¤® ­ã«ï ¨«¨ ¥á«¨ ¬®¤¥«ì ¯à®è«  § ¤ ­­®¥
à ááâ®ï­¨¥.
à¨ ¨áá«¥¤®¢ ­¨¨ ¢«¨ï­¨ï à ª¥â­®£® ¤¢¨£ â¥«ï
­  ¤ «ì­®áâì 室  ¬®¤¥«¥© ¢ ª ç¥á⢥ ¡ §®¢ëå ¡ë-
«¨ ¢ë¡à ­ë âਠ¬®¤¥«¨ ¯à¥¤ë¤ã饩 á¥à¨¨, ¤¢¥
¤«¨­®© 250 ¬¬ ¨ ®¤­  ¤«¨­®© 150 ¬¬. ‚ àì¨à®-
¢ «¨áì ­ ç «ì­ ï ᪮à®áâì ¬®¤¥«¨ (1200, 1000, 800
¨ 600 ¬/á) ¨ 㤥«ì­ë© ¨¬¯ã«ìá ⮯«¨¢  (200, 400
¨ 600 ªƒá/(ª£/á)). «®â­®áâì ⮯«¨¢  ¢® ¢á¥å á«ã-
ç ïå ¯à¨­¨¬ « áì à ¢­®© 1:85£=á¬
3
.
‚ à áç¥â å â ª¦¥ ¯à¨­¨¬ «®áì, çâ® £®à¥­¨¥
¯à®¨á室¨â á ¯®áâ®ï­­®© ᪮à®áâìî (ª®íää¨æ¨¥­â
a
f1
¢ ãà ¢­¥­¨¨ (13) à ¢¥­ 0). ‚¥«¨ç¨­  ª®íää¨-
樥­â  a
f0
¢ë¡¨à « áì â ª¨¬ ®¡à §®¬, çâ®¡ë § 
¢à¥¬ï ¤¢¨¦¥­¨ï ¢á¥ ⮯«¨¢® ᣮ५®. ‡­ ç¥­¨¥
¥£® ¡ë«® à §«¨ç­ë¬ ¨ á®áâ ¢«ï«® ®â 2 ¤® 12 ¤«ï
à §­ëå ¬®¤¥«¥©, â. ¥. £®à¥­¨¥ ⮯«¨¢  ¯à®¤®«-
¦ «®áì 1/2 { 1/12 á. ‚ í⮬ á«ãç ¥ ¡®«ìèãî ç áâì
¯ã⨠¬®¤¥«ì ¯à®å®¤¨«  á à ¡®â î騬 ¤¢¨£ â¥«¥¬.
¥§ã«ìâ âë à áç¥â®¢ ¤«ï ®¤­®© ¨§ ¬®¤¥«¥© ¯à¨-
¢¥¤¥­ë ­  à¨á. 3.
‚¨¤­®, çâ® ¯à¨ 㤥«ì­®¬ ¨¬¯ã«ìᥠQ
f
= 200 § -
¬¥­  ¬ â¥à¨ «  ¬®¤¥«¨ ⮯«¨¢®¬ ­¥ ¤ ¥â ¢ë¨£àë-
è  ¢ ¤ «ì­®áâ¨. ’ ª®© ¦¥ १ã«ìâ â ¯®«ã祭 ¤«ï
¤àã£¨å ¬®¤¥«¥©. ®«¥¥ íä䥪⨢­®¥ ⮯«¨¢® ¤ ¥â
®¯à¥¤¥«¥­­ë© ¢ë¨£àëè ¢ ¤ «ì­®á⨠{ ®â 30% ¯à¨
¡®«ì让 ­ ç «ì­®© ᪮à®á⨠¤® 150% ¯à¨ ¬ «®©.
„«ï ¡®«¥¥ «¥£ª¨å ¬®¤¥«¥© (­ ¯à¨¬¥à,  «î¬¨­¨-
¥¢ëå) १ã«ìâ âë ¡ë«¨ ¡ë ¤à㣨¬¨.
à¥¤áâ ¢«ï¥â ¨­â¥à¥á ¨áá«¥¤®¢ âì ¢«¨ï­¨¥ à¥-
¦¨¬  à ¡®âë ¤¢¨£ â¥«ï ­  ¯à®å®¤¨¬®¥ ¬®¤¥«ìî
à ááâ®ï­¨¥ ¨ ­ ©â¨ ®¯â¨¬ «ì­ë© ०¨¬.
à¥¤¯®«®¦¨¬, çâ® ¤¢¨¦¥­¨¥ ¬®¤¥«¨ ­  ¤¨áâ ­-
樨 á®á⮨⠨§ âà¥å ãç á⪮¢: 1.  ç «ì­ë© ãç -
á⮪ ¤¢¨¦¥­¨ï ¯® ¨­¥à樨 ¡¥§ â; 2.  ¢­®¬¥à-
­®¥ ¤¢¨¦¥­¨¥ ᮠ᪮à®áâìî V
1
¯à¨ â, à ¢­®©
ᮯà®â¨¢«¥­¨î; 3. ‡ ª«îç¨â¥«ì­ë© ãç á⮪ ¤¢¨-
¦¥­¨ï ¯® ¨­¥à樨.
 ááâ®ï­¨¥, ¯à®å®¤¨¬®¥ ­  ª ¦¤®¬ ãç á⪥, § -
¢¨á¨â ®â ᪮à®á⨠V
1
.
„¢¨¦¥­¨¥ ­  ãç á⪠å 1 ¨ 3 ®¯¨á뢠¥âáï ãà ¢-
­¥­¨ï¬¨ à §¤¥«  1.
  ¢â®à®¬ ãç á⪥ ¤¢¨¦¥­¨¥ à ¢­®¬¥à­®, â
à ¢­  ᮯà®â¨¢«¥­¨î,   ¢à¥¬ï £®à¥­¨ï ⮯«¨¢ 
¬®¦­® ®¯à¥¤¥«¨âì ¨§ ¢ëà ¦¥­¨ï (14). ’®£¤  ¤«ï
¯à®©¤¥­­®£® ­  í⮬ ãç á⪥ ¯ã⨠¯®«ã稬:
S
2
=
Q
f
m
f0
kmV
2
1
: (15)
’ ª¨¬ ®¡à §®¬, ¯ãâì, ¯à®å®¤¨¬ë© ­  1 ¨ 2
ãç á⪠å, 㢥«¨ç¨¢ ¥âáï á 㬥­ì襭¨¥¬ V
1
. ãâì,
¯à®å®¤¨¬ë© ­  3 ãç á⪥, 㬥­ìè ¥âáï, ®¤­ ª®
á㬬  S
1
+S
2
®â V
1
­¥ § ¢¨á¨â:
S
1
+S
3
=
1
k
ln
V
0
V
e
; (16)
£¤¥ V
e
{ ªà¨â¨ç¥áª ï (ª®­¥ç­ ï) ᪮à®áâì.
‘«¥¤®¢ â¥«ì­®, ®¡é¥¥ à ááâ®ï­¨¥ 㢥«¨ç¨¢ ¥â-
áï á 㬥­ì襭¨¥¬ V
1
.
®í⮬㠤¢¨£ â¥«ì ¤®«¦¥­ ¢ª«îç âìáï ¯à¨ áª®-
à®áâ¨, «¨èì ­¥¬­®£® ¯à¥¢ëè î饩 ªà¨â¨ç¥áªãî.
—¨á«¥­­ë¥ à áç¥âë ¯®¤â¢¥à¤¨«¨ á¯à ¢¥¤«¨¢®áâì
í⮩ á奬ë. ‚® ¢á¥å á«ãç ïå, ª®£¤  ⮯«¨¢® ãᯥ-
¢ «® ¯®«­®áâìî ᣮà¥âì ¤® ⮣®, ª ª ᪮à®áâì ¬®-
¤¥«¨ 㯠«  ¤® ªà¨â¨ç¥áª®© ¢¥«¨ç¨­ë, ¤ «ì­®áâì
¢®§à áâ « á 㢥«¨ç¥­¨¥¬ ¢à¥¬¥­¨ ¢ª«î祭¨ï ¤¢¨-
£ â¥«ï.
  à¨á. 4 ¯®ª § ­  § ¢¨á¨¬®áâì ᪮à®á⨠®â
¯à®©¤¥­­®£® ¯ã⨠¤«ï ¬®¤¥«¨ á à ¡®â î騬 ¤¢¨-
£ â¥«¥¬ ¯à¨ áâ à⮢®¬ ¢à¥¬¥­¨ 0.6 á (ªà¨¢ ï 1),
0.2 á (ªà¨¢ ï 2), ¤«ï ¨á室­®© ᯫ®è­®© ¬®¤¥«¨
(ªà¨¢ ï 3), ¯®«®© ¬®¤¥«¨ ¡¥§ ¤¢¨£ â¥«ï (ªà¨¢ ï 4).
‚¨¤­®, çâ® ¯à¨ à ­­¥¬ ¢ª«î祭¨¨ ¤¢¨£ â¥«ï ¬®-
¤¥«ì ¯à®å®¤¨â ­¥¡®«ì讥 à ááâ®ï­¨¥ á ¯®¢ë襭-
­®© ᪮à®áâìî, § â¥¬ ¡ëáâà® â®à¬®§¨âáï.
ˆáá«¥¤®¢ ­¨¥ § ¢¨á¨¬®á⨠¤ «ì­®á⨠®â ᪮à®-
á⨠£®à¥­¨ï ⮯«¨¢  ¯à¨ 䨪á¨à®¢ ­­®¬ ¢à¥¬¥­¨
¢ª«î祭¨ï ¯®ª § «®,çâ® ¤ «ì­®áâì ¯« ¢­® á­¨¦ -
¥âáï ¯à¨ ã¢¥«¨ç¥­¨¨ ᪮à®á⨠£®à¥­¨ï. Ž¤­ ª®,
68 ‘. ˆ. ã⨫¨­
ISSN 1561-9087 à¨ª« ¤­  £÷¤à®¬¥å ­÷ª . 2000. ’®¬ 2 (74), N 3. ‘. 65{74
¨á. 4. ‡ ¢¨á¨¬®áâì ᪮à®á⨠®â ¯ãâ¨
¯à¨ à §«¨ç­®¬ ¢à¥¬¥­¨ § ¯ã᪠ ¤¢¨£ â¥«ï
¨á. 5. ‡ ¢¨á¨¬®áâì ᪮à®á⨠®â ¯ãâ¨
¯à¨ à §«¨ç­®© ᪮à®á⨠£®à¥­¨ï ⮯«¨¢ 
¯à¨ ®ç¥­ì ¬ «®© ᪮à®á⨠£®à¥­¨ï â ®ª §ë¢ -
¥âáï ­¥¤®áâ â®ç­®© ¤«ï ¯®¤¤¥à¦ ­¨ï ¯®áâ®ï­­®©
᪮à®á⨠¬®¤¥«¨, ¯®á«¥¤­ïï â®à¬®§¨âáï ¨ ¤ «ì-
­®áâì १ª® ᮪à é ¥âáï.
  à¨á. 5 ¯®ª § ­® ¨§¬¥­¥­¨¥ ᪮à®á⨠¬®¤¥«¨
¯à¨ à §­®© ᪮à®á⨠£®à¥­¨ï ⮯«¨¢ . Šà¨¢ ï 1
ᮮ⢥âáâ¢ã¥â §­ ç¥­¨îa
f0
= 1:75á
BnZr1
(¬ ªá¨¬ã¬
¤ «ì­®áâ¨), ¯à¨ í⮬ â ãà ¢­®¢¥è¨¢ ¥â ᮯà®-
⨢«¥­¨¥ ¨ ¬®¤¥«ì¯®á«¥ ¢ª«î祭¨ï ¤¢¨£ â¥«ï ¤¢¨-
¦¥âáï à ¢­®¬¥à­®. à¨ a
f0
= 2:5á
BnZr1
(ªà¨¢ ï 2)
᪮à®áâì ¬®¤¥«¨ 㢥«¨ç¨¢ ¥âáï, ­® ¢à¥¬ï à ¡®âë
¤¢¨£ â¥«ï 㬥­ì訫®áì, ¨ ¤ «ì­®áâì ¨§¬¥­¨« áì
­¥§­ ç¨â¥«ì­®. à¨ a
f0
= 1:5á
BnZr1
(ªà¨¢ ï 3) ¬®-
¤¥«ì â¥àï¥â ᪮à®áâì ¨ ¯à¨ à ¡®â î饬 ¤¢¨£ â¥-
«¥, ç⮠᪠§ «®áì ­  ¤ «ì­®áâ¨.  ­­¥¥ ¢ª«î祭¨¥
¤¢¨£ â¥«ï (ªà¨¢ ï 4) â ª¦¥ ¢¥¤¥â ª ¯®â¥à¥ ¤ «ì-
­®áâ¨.
 áç¥âë ¯®ª § «¨, çâ® ®¯â¨¬¨§ æ¨ï ०¨¬ 
à ¡®âë ¤¢¨£ â¥«ï ¯®§¢®«ï¥â ¯®¢ëá¨âì ¤ «ì­®áâì
­  10 %.
Ž‘Ž…Ž‘’ˆ ‚Ž‡Œ“™…ŽƒŽ „‚ˆ-
†…ˆŸ ŒŽ„…‹ˆ
Ž¯¨á ­¨¥ ¬¥â®¤¨ª¨¨áá« ¥¤®¢ ­¨ï
ˆáá«¥¤®¢ ­¨¥ ¢®§¬ã饭­®£® ¤¢¨¦¥­¨ï ¬®¤¥«¨
¯à®¢®¤¨«®áì ¬¥â®¤®¬ ç¨á«¥­­®£® ¨­â¥£à¨à®¢ ­¨ï
ãà ¢­¥­¨© ¤¢¨¦¥­¨ï ¯à¨ § ¤ ­­ëå ­ ç «ì­ëå
ãá«®¢¨ïå. â¨ ãà ¢­¥­¨ï ¢ª«îç îâ [3]:
 ) ᮡá⢥­­® ãà ¢­¥­¨ï ¤¢¨¦¥­¨ï;
¡) ãà ¢­¥­¨ï ¤«ïà áç¥â  à §¬¥à®¢,ä®à¬ë ¨ ¯®-
«®¦¥­¨ï ª ¢¥à­ë;
¢) ãà ¢­¥­¨ï, á¢ï§ë¢ î騥 £¨¤à®¤¨­ ¬¨ç¥áª¨¥
ᨫë á ¯ à ¬¥âà ¬¨ ª ¢¥à­ë ¨ á ¯ à ¬¥âà ¬¨
¤¢¨¦¥­¨ï ⥫ .
“à ¢­¥­¨ï ¤¢¨¦¥­¨ï ®¡é¥¨§¢¥áâ­ë [4].
“à ¢­¥­¨ï ¤«ï à áç¥â  à §¬¥à®¢ ª ¢¥à­ë
¢ª«îç îâ ä®à¬ã«ë ¤«ï à áç¥â  ®á­®¢­ëå ¥¥ à §-
¬¥à®¢ (à ¤¨ãá  ­ ¨¡®«ì襣® á¥ç¥­¨ï R
c
¨ ¯®«ã-
¤«¨­ëL
c
) ¨ à ¤¨ãá  ­  § ¤ ­­®¬ à ááâ®ï­¨¨ x®â
ª ¢¨â â®à . ®á«¥¤­¨© ®¯à¥¤¥«ï¥âáï ᮮ⭮襭¨-
¥¬ [1]
R(x) = R
c
s
1BnZr
2
j 1BnZr
t
x

V(tBnZrt
x
)
L
c
(tBnZrt
x
)
j
2=
; (17)
£¤¥ t
x
{ ¢à¥¬ï, ¯à®è¥¤è¥¥ á ¬®¬¥­â  ®¡à §®¢ ­¨ï
à áᬠâਢ ¥¬®£® á¥ç¥­¨ï ª ¢¥à­ë;{ ¯®¯à ¢®ç-
­ë© ª®íää¨æ¨¥­â, ª®â®àë© ¯à¨­¨¬ «áï à ¢­ë¬ 1.
â  ä®à¬ã«  á¯à ¢¥¤«¨¢  ¯à¨ x> 2r
n
.
®«®¦¥­¨¥ ®á¨ ª ¢¥à­ë ®¯à¥¤¥«ï¥âáï:
{ âà ¥ªâ®à¨¥© 業âà  ª ¢¨â â®à ;
{ ᬥ饭¨¥¬ ª ¢¥à­ë ¯®¤ ¤¥©á⢨¥¬ á¨«ë €à-
娬¥¤ ;
{ ᬥ饭¨¥¬, ¢ë§¢ ­­ë¬ ­ «¨ç¨¥¬ ¯®¤ê¥¬­®©
á¨«ë ­  ª ¢¨â â®à¥.
®«®¦¥­¨¥ 業âà  ª ¢¨â â®à  ¢ ¬®¬¥­â ¢à¥¬¥-
­¨ t ®¯à¥¤¥«ï¥âáï § ¢¨á¨¬®áâìî
y
n
(t) = y
m
(t) + (t)L
n
; (18)
£¤¥ y
m
{ ª®®¤¨­ â  業âà  ¨­¥à樨 ¬®¤¥«¨; L
n
{
à ááâ®ï­¨¥ ®â ª ¢¨â â®à ¤®æ¥­âà  ¨­¥à樨;  (t)
{ 㣮« â ­£ ¦ .
‘«¥¤®¢ â¥«ì­®, ¨¬¥ï § ¢¨á¨¬®á⨠y
m
(t) ¨  (t)
¤«ï ­¥ª®â®à®£® ¯à®¬¥¦ã⪠ ¢à¥¬¥­¨, ¬®¦­® ¢®á-
áâ ­®¢¨âì âà ¥ªâ®à¨î 業âà  ª ¢¨â â®à , ª®â®-
à ï ¢ ¯¥à¢®¬ ¯à¨¡«¨¦¥­¨¨ ï¥âáï £¥®¬¥âà¨ç¥-
᪨¬ ¬¥á⮬ 業â஢ á¥ç¥­¨© ª ¢¥à­ë.
‘¨«  ¯« ¢ãç¥á⨠ª ¢¥à­ë ¨ ¯®¤ê¥¬­ ï ᨫ  ª -
¢¨â â®à  ¢ë§ë¢ îâ ᬥ饭¨¥ ®á¨ ª ¢¥à­ë ®â
âà ¥ªâ®à¨¨ ª ¢¨â â®à . ”®à¬ã«ë ¤«ï à áç¥â 
¢¥«¨ç¨­ë ¨ ᪮à®á⨠í⮣® ᬥ饭¨ï ¯à¨¢¥¤¥­ë
¢ [1]. Ž­¨ ᮤ¥à¦ â ¯ à ¬¥âàë ¤¢¨¦¥­¨ï ⥫ 
‘. ˆ. ã⨫¨­ 69
ISSN 1561-9087 à¨ª« ¤­  £÷¤à®¬¥å ­÷ª . 2000. ’®¬ 2 (74), N 3. ‘. 65{74
¢ ¬®¬¥­â ®¡à §®¢ ­¨ï à áᬠâਢ ¥¬®£® á¥ç¥­¨ï
ª ¢¥à­ë ¨ ¯ à ¬¥âàë í⮣® á¥ç¥­¨ï ¢ à áᬠâà¨-
¢ ¥¬ë© ¬®¬¥­â ¢à¥¬¥­¨.
’ ª¨¬ ®¡à §®¬, ª®®à¤¨­ â  業âà  ª ¢¥à­ë y
c
®¯à¥¤¥«ï¥âáï ᮮ⭮襭¨¥¬
y
c
(t) = y
m
(tBnZrt
x
)+ (tBnZrt
x
)L
n
+Y
cg
(x)+
+F
ny
(tBnZrt
x
)Y
cy
(x;t); (19)
  ᪮à®áâì ¥£® ᬥ饭¨ï § ¢¨á¨¬®áâìî
V
c
(t) = V
cg
(x)+F
ny
(tBnZrt
x
)Y

cy
(x;t); (20)
£¤¥ Y
cg
(x);V
cg
(x) { ᬥ饭¨¥ ¨ ᪮à®áâì ᬥ饭¨ï
業âà  ª ¢¥à­ë ¯®¤ ¤¥©á⢨¥¬ á¨«ë ¯« ¢ãç¥áâ¨;
F
ny
(tBnZrt
x
) { ¯®¤ê¥¬­ ï ᨫ  ª ¢¨â â®à  ¢ ¬®¬¥­â
®¡à §®¢ ­¨ï á¥ç¥­¨ï ª ¢¥à­ë; Y
cy
(x;t) { ¬­®¦¨-
⥫ì, § ¢¨áï騩 ®â ä®à¬ë ª ¢¥à­ë.
Š®®à¤¨­ â  â®çª¨ x ­  ®á¨ ¬®¤¥«¨ ¢ ¬®¬¥­â t
à ¢­ 
y
(
x;t) = y
m
(t) + (t)(L
n
BnZrx) (21)
¨ ¥¥ ᪮à®áâì
V
y
(x;t) = V
ym
(t)+ 
(L
n
BnZrx); (22)
£¤¥ 
 { 㣫®¢ ï ᪮à®áâì ¬®¤¥«¨.
Žâá ­ å®¤¨¬ ¯®£à㦥­¨¥ ¯à®¨§¢®«ì­®£® á¥-
祭¨ï ¬®¤¥«¨ ¢ ­¨¦­îî ¨«¨ ¢¥àå­îî £à ­¨æë ª -
¢¥à­ë ¨ ®â­®á¨â¥«ì­ãî ᪮à®áâì á¥ç¥­¨ï ¬®¤¥«¨
¨ á¥ç¥­¨ï ª ¢¥à­ë.
à¨¢¥¤¥­­ë¥ ᮮ⭮襭¨ï á¯à ¢¥¤«¨¢ë ¤«ï «î-
¡®£® § ª®­  ¤¢¨¦¥­¨ï ¬®¤¥«¨. ‚ ç áâ­ëå á«ãç ïå
¤¢¨¦¥­¨ï á ¯®áâ®ï­­ë¬ 㣫®¬  â ª¨ ¨«¨ á ¯®áâ®-
ï­­®© 㣫®¢®© ᪮à®áâìî ¬®¦­® ¯®«ãç¨âì ¡®«¥¥
㤮¡­ë¥ ¤«ï ¯à ªâ¨ç¥áª¨å à áç¥â®¢ ¢ëà ¦¥­¨ï.
ˆá¯®«ì§ãï á¢ï§ ­­ãî á ¬®¤¥«ìî á¨á⥬㠪®®à-
¤¨­ â [4] ¨ ¯à¥­¥¡à¥£ ï á®áâ ¢«ïî騬¨, á¢ï§ ­-
­ë¬¨ á ¤¢¨¦¥­¨¥¬ ª ¢¥à­ë ¯®¤ ¤¥©á⢨¥¬ ᨫë
¯« ¢ãç¥á⨠¨ ¯®¤ê¥¬­®© á¨«ë ª ¢¨â â®à , ¯®«ã-
稬 á«¥¤ãî饥 ¢ëà ¦¥­¨¥ ¤«ï ᪮à®á⨠業âà 
á¥ç¥­¨ï ª ¢¥à­ë ®â­®á¨â¥«ì­® ¬®¤¥«¨:
u
á
(x;t) = V
m
(t) BnZr
(t)(L
n
BnZrx); (23)
£¤¥ 
m
{ 㣮«  â ª¨ ¢ 業âॠ¨­¥à樨 ¬®¤¥«¨; x
{ à ááâ®ï­¨¥ ®â ª ¢¨â â®à  ¤® à áᬠâਢ ¥¬®£®
á¥ç¥­¨ï.
à¨ ¤¢¨¦¥­¨¨ á ¯®áâ®ï­­ë¬ 㣫®¬  â ª¨ ¡¥§
㣫®¢®© ᪮à®á⨠(¯àאַ«¨­¥©­®¥ ¤¢¨¦¥­¨¥) ¨­-
⥣à¨à®¢ ­¨¥ ᮮ⭮襭¨ï (23) ¯à¨¢®¤¨â ª á«¥¤ã-
î饬㠢ëà ¦¥­¨î ¤«ï à ááâ®ï­¨ï ¬¥¦¤ã ®áﬨ
¬®¤¥«¨ ¨ ª ¢¥à­ë a
c
:
a
c
(x) = 
m
x: (24)
…᫨ 㣮«  â ª¨ ¨ 㣫®¢ ï ᪮à®áâì ¯®áâ®ï­­ë
(à ¢­®¬¥à­®¥ ¤¢¨¦¥­¨¥ ¯® ®ªà㦭®áâ¨), â® ¯®«ã-
稬:
a
c
(x) =
m
xBnZr


V
(L
n
xBnZr
x
2
2
): (25)
®«ì让 ¨­â¥à¥á ¯à¥¤áâ ¢«ï¥â ¯àאַ«¨­¥©­®¥
¤¢¨¦¥­¨¥ á ¯®áâ®ï­­®© 㣫®¢®© ᪮à®áâìî. ‚
í⮬ á«ãç ¥ 㣮«  â ª¨ ¡ã¤¥â ¯¥à¥¬¥­­ë¬,   ¢ë-
à ¦¥­¨¥ ¤«ï à ááâ®ï­¨ï a
c
¨¬¥¥â ¢¨¤
a
c
(x;t) = x[
m
(t) BnZr


V
(L
n
BnZrx)]; (26)
£¤¥ 
m
(t) { 㣮«  â ª¨ ¢ 業âॠ¨­¥à樨 ¬®¤¥«¨ ¢
à áᬠâਢ ¥¬ë© ¬®¬¥­â ¢à¥¬¥­¨.
®«ã祭­ë¥ ᮮ⭮襭¨ï ¯®§¢®«ïî⠮業¨âì
¢«¨ï­¨¥ ¢®§¬ã饭¨©, ¢®§­¨ª îé¨å ¯à¨ ¤¢¨¦¥­¨¨
¬®¤¥«¨, ­  ¯¥à¥à á¯à¥¤¥«¥­¨¥ § §®à®¢ ¬¥¦¤ã ¬®-
¤¥«ìî ¨ £à ­¨æ¥© ª ¢¥à­ë.
ƒ¨¤à®¤¨­ ¬¨ç¥áª¨¥ ᨫë
Žá­®¢­ë¬¨ £¨¤à®¤¨­ ¬¨ç¥áª¨¬¨ ᨫ ¬¨, ¤¥©-
áâ¢ãî騬¨ ­  ¬®¤¥«ì ¢ á«ãç ¥, ¥á«¨ ¤¨ ¬¥âà «î-
¡®£® ¥¥ á¥ç¥­¨ï ¬¥­ìè¥ ¤¨ ¬¥âà  á®®â¢¥âáâ¢ãî-
饣® á¥ç¥­¨ï ª ¢¥à­ë, ïîâáï ᨫ  ­  ª ¢¨â -
â®à¥ ¨ ᨫ , ¢®§­¨ª îé ï ¯à¨ ª®­â ªâ¥ ¡®ª®¢®©
¯®¢¥àå­®á⨠⥫  á £à ­¨æ¥© ª ¢¥à­ë.
‘¨« , ¤¥©áâ¢ãîé ï ­  ª ¢¨â â®à,§ ¢¨á¨â [1]®â
㣫  ¬¥¦¤ã ¢¥ªâ®à®¬ ᪮à®á⨠ª ¢¨â â®à  ®â­®-
á¨â¥«ì­® ¦¨¤ª®á⨠¨ ­®à¬ «ìî ª ª ¢¨â â®àã. ‚
á«ãç ¥ ¨¤¥ «ì­®© ¦¨¤ª®á⨠¨ ¯«®áª®£® ª ¢¨â â®-
à , ¯¥à¯¥­¤¨ªã«ïà­®£® ®á¨ ¬®¤¥«¨, ®­  ᢮¤¨âáï ª
ᨫ¥ ᮯà®â¨¢«¥­¨ï.
à¨ ᨬ¬¥âà¨ç­®¬ ®¡â¥ª ­¨¨ â ª®£® ª ¢¨â â®-
à  ¤¥©áâ¢ãîé ï ­  ­¥£® ᨫ  ­ ¯à ¢«¥­  ¯® ®á¨
¬®¤¥«¨ ¨ ­¥ ᮧ¤ ¥â ¬®¬¥­â  ®â­®á¨â¥«ì­® ¥¥ 業-
âà  ¨­¥à樨. ‚ ¨¤¥ «ì­®© ¦¨¤ª®á⨠­ àã襭¨¥
ᨬ¬¥âਨ ®¡â¥ª ­¨ï ­¥ ¯à¨¢®¤¨âª¯®ï¢«¥­¨î á®-
áâ ¢«ïî饩, ¯¥à¯¥­¤¨ªã«ïà­®© ®á¨ ¬®¤¥«¨. ‚®§-
¬®¦­® ⮫쪮 ᬥ饭¨¥ «¨­¨¨ ¤¥©á⢨ï í⮩ ᨫë
­  ¢¥«¨ç¨­ã, ­¥ ¯à¥¢ëè îéãî à ¤¨ãá  ª ¢¨â â®-
à .
‚ ॠ«ì­®© ¦¨¤ª®á⨠¢®§¬®¦­® ¯®ï¢«¥­¨¥ ¯®¯¥-
à¥ç­®© á¨«ë ¢á«¥¤á⢨¥  á¨¬¬¥âਨ ᨫ â७¨ï ­ 
ª ¢¨â®â®à¥.
Š ᮦ «¥­¨î, ­ ¬ ­¥ ¨§¢¥áâ­ë ç¨á«¥­­ë¥ §­ -
祭¨ï ª®íää¨æ¨¥­â®¢, ãç¨â뢠îé¨å ¤¢ ã¯®¬ï­ã-
âëå íä䥪â .
‘¨«ë, ¢®§­¨ª î騥 ­  ¡®ª®¢®©¯®¢¥àå­®á⨠¬®-
¤¥«¨ ¢ á«ãç ¥, ª®£¤  ¥¥ à ¤¨ãá ¬¥­ìè¥ à ¤¨ãá 
ª ¢¥à­ë, ®¯à¥¤¥«ïîâáï ¯® ⥮ਨ £«¨áá¨à®¢ ­¨ï
â®­ª®£® ⥫  [23], ¯à¨ í⮬ ¨á¯®«ì§ã¥âáï à¥è¥­¨¥
§ ¤ ç¨ ® ¯®£à㦥­¨¨ ªà㣮¢®© ¤ã¦ª¨ ¢ ᦨ¬ î-
éãîáï ªà㣮¢ãî ᢮¡®¤­ãî ¯®¢¥àå­®áâì. ‚ à¥-
§ã«ìâ â¥ ¯®«ãç ¥âáï ¯à®á⮥ ¢ëà ¦¥­¨¥ ¤«ï á¨-
«ë, ¤¥©áâ¢ãî饩 ­  âã ç áâì ¬®¤¥«¨, ª®â®à ï à á-
70 ‘. ˆ. ã⨫¨­
ISSN 1561-9087 à¨ª« ¤­  £÷¤à®¬¥å ­÷ª . 2000. ’®¬ 2 (74), N 3. ‘. 65{74
¯®«®¦¥­  ¢¯¥à¥¤¨ à áᬠâਢ ¥¬®£® á¥ç¥­¨ï, ç¥-
१ ᪮à®áâì ®â­®á¨â¥«ì­®£® ᬥ饭¨ï ⥫  ¨ ª -
¢¥à­ë U
1
, ᪮à®áâì ᦠâ¨ï á¥ç¥­¨ï ª ¢¥à­ë U
2
,
á।­îî ¢¥«¨ç¨­ã § §®à  ¬¥¦¤ã £à ­¨æ ¬¨ ¬®¤¥-
«¨ ¨ ª ¢¥à­ë ¨ ¯®£à㦥­¨¥ ­¨¦­¥© â®çª¨ á¥ç¥­¨ï
¬®¤¥«¨ ®â­®á¨â¥«ì­® ­¥¢®§¬ã饭­®© £à ­¨æë ª -
¢¥à­ë h.
„«ï ­¥æ¨«¨­¤à¨ç¥áª¨å ⥫ ᪮à®áâì U
2
á«¥¤ã¥â
®¯à¥¤¥«ïâì á ãç¥â®¬ 㣫  à áè¨à¥­¨ï ¯®¢¥àå­®-
á⨠⥫ .
‚¥«¨ç¨­ë h ¨ U
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§ ¢¨áï⠮⠯।ë¤ã饣® ¤¢¨-
¦¥­¨ï ¬®¤¥«¨, á¬. ãà ¢­¥­¨ï (21) ¨ (22). ‚ á¨-
«ã í⮣® á¨á⥬  ãà ¢­¥­¨© ¤¢¨¦¥­¨ï á㯥ઠ¢¨-
â¨àãî饣® ⥫  ï¥âáï á¨á⥬®© ãà ¢­¥­¨© á
§ ¯ §¤ë¢ ­¨¥¬ [6], ¨ ¤«ï ®¯à¥¤¥«¥­­®á⨠à¥è¥­¨ï
­ ç «ì­ë¥ ãá«®¢¨ï ¤®«¦­ë ¡ëâì § ¤ ­ë ­  ®â१-
ª¥ ¯ãâ¨, à ¢­®¬ ¤«¨­¥ ¬®¤¥«¨.
‚ëà ¦¥­¨¥ ¤«ï £¨¤à®¤¨­ ¬¨ç¥áª®£® ¬®¬¥­â ,
¢®§­¨ª î饣® ¯à¨ £«¨áá¨à®¢ ­¨¨ ¬®¤¥«¨ ¯® £à -
­¨æ¥ ª ¢¥à­ë, ¯®«ãç ¥âáï ¤®áâ â®ç­® á«®¦­ë¬.
®í⮬ã à áç¥â ¥£® ®áãé¥á⢫ï¥âáï ¬¥â®¤®¬ ç¨-
á«¥­­®£® ¨­â¥£à¨à®¢ ­¨ï.
„«ï à áç¥â  ¤¢¨¦¥­¨ï á㯥ઠ¢¨â¨àãîé¨å ¬®-
¤¥«¥© ¯® ¯à¨¢¥¤¥­­ë¬ ãà ¢­¥­¨ï¬ ¡ë«  ࠧࠡ®-
â ­  ¯à®£à ¬¬  DCAVM-i.for, ª®â®à ï ¯®§¢®«ï¥â
à ááç¨â뢠âì ¤¢¨¦¥­¨¥ ¬®¤¥«¥© ¢ ª ¢¥à­ å, ®¡à -
§ãîé¨åáï ª ª ¯à¨ ®ç¥­ì ­¨§ª¨å, â ª ¨ ¯à¨ ¢ëá®-
ª¨å ç¨á« å ª ¢¨â æ¨¨. à¨ ®ç¥­ì ­¨§ª¨å ç¨á« å
ª ¢¨â æ¨¨ ¬®¤¥«ì à á¯®«®¦¥­  ¢ ¯¥à¥¤­¥© ç áâ¨
ª ¢¥à­ë, ¯à¨ç¥¬ 㣮« ¬¥¦¤ã ®¡à §ãî饩 ¯®¢¥àå-
­®á⨠¬®¤¥«¨ ¨ £à ­¨æ¥© ª ¢¥à­ë ®ç¥­ì ¬ «. â®
ᮧ¤ ¥â ®¯à¥¤¥«¥­­ë¥ âà㤭®á⨠¯à¨ à áç¥â¥ ¤«¨-
­ë ᬮ祭­®© ç á⨠¬®¤¥«¨ ¨ ¯à®¤®«ì­®£® ¬®¬¥­-
â . ‚ ¯à®£à ¬¬¥ DCAVM-i à áç¥â ¢§ ¨¬­®£®¯®-
«®¦¥­¨ï ¬®¤¥«¨ ¨ ª ¢¥à­ë ¯à®¨§¢®¤¨âáï ¤«ï ­¥-
᪮«ìª¨å ¯®¯¥à¥ç­ëå á¥ç¥­¨©, çâ® ¯®¢ë蠥⠥£®
â®ç­®áâì.
ˆáá«¥¤®¢ ­¨¥ ¯®¢¥¤¥­¨ï ¬®¤¥«¥©
„«ï áà ¢­¨â¥«ì­®©®æ¥­ª¨ ¯®¢¥¤¥­¨ï à §«¨ç­ëå
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¤¢¨¦¥­¨ï ¯à¨ ®¤¨­ ª®¢ëå ­ ç «ì­ëå ãá«®¢¨ïå.
 ç «ì­ë¥ ãá«®¢¨ï ¯®¤¡¨à «¨áì â ª¨¬ ®¡à §®¬,
çâ®¡ë ¢ ­ ç «ì­ë© ¬®¬¥­â ¢à¥¬¥­¨ ¬®¤¥«ì ¤¢¨£ -
« áì ¢ £®à¨§®­â «ì­®¬ ­ ¯à ¢«¥­¨¨, ¨¬¥ï ­¥¡®«ì-
让 㣮« â ­£ ¦  ¨ ­¥¡®«ìèãî 㣫®¢ãî ᪮à®áâì.
‡­ ª ­ ç «ì­®© 㣫®¢®© ᪮à®á⨠¢ë¡¨à «áï â -
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â ­£ ¦  㢥«¨ç¨¢ « áì. —¥à¥§ ­¥ª®â®à®¥ ¢à¥¬ï
ª®à¬®¢ ï ç áâì ¬®¤¥«¨ ª á « áì £à ­¨æë ª ¢¥à-
­ë ¨ ­ ç¨­ «®áì ª®«¥¡ â¥«ì­®¥ ¤¢¨¦¥­¨¥ (à¨á. 6).
Ž¡ëç­® ¢­ ç «¥  ¬¯«¨â㤠 ª®«¥¡ ­¨© § ¬¥â­® ¨§-
¬¥­ï« áì, ­®, ¤®á⨣­ã¢ ­¥ª®â®à®© ¢¥«¨ç¨­ë, áâ -
¡¨«¨§¨à®¢ « áì.   à¨á. 6 ¯à¨¢¥¤¥­ ¯à¨¬¥à § ¢¨-
ᨬ®á⨠㣫  â ­£ ¦ , 㣫®¢®© ᪮à®áâ¨, ¯®¤ê¥¬-
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¨á. 7. ” §®¢ ï âà ¥ªâ®à¨ï ª®«¥¡ ­¨© ¬®¤¥«¨ ¢
ª ¢¥à­¥
­®© á¨«ë ¨ ¯à®¤®«ì­®£® ¬®¬¥­â  ®â ¯à®©¤¥­­®£®
¯ãâ¨.
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§®¢ë¥ âà ¥ªâ®à¨¨ [7], â. ¥. § ¢¨á¨¬®áâì 㣫®¢®©
᪮à®á⨠®â 㣫  â ­£ ¦  (à¨á. 7). Ž¡ëç­® ä §®-
¢ë¥ âà ¥ªâ®à¨¨ ¯à¥¤áâ ¢«ïîâ ᮡ®© ᯨࠫ¨, ª®-
â®àë¥ á¦¨¬ îâáï ¯à¨ ãá⮩稢®¬ ¤¢¨¦¥­¨¨ ¨«¨
à áè¨àïîâáï ¯à¨ ­¥ãá⮩稢®¬. ” §®¢ ï âà ¥ª-
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⮪®«¥¡ â¥«ì­®¬ã ०¨¬ã. „¢¨¦¥­¨¥ ¯® ä §®¢®©
âà ¥ªâ®à¨¨ ¯à®¨á室¨â ¯® ç á®¢®© áâ५ª¥.
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¥¬­ ï ᨫ  ¨ ¯à®¤®«ì­ë© ¬®¬¥­â.
‚ á«ãç ¥ ¤¢¨¦¥­¨ï ¬®¤¥«¨ ¢ ª ¢¥à­¥ á ¡®«ì訬
§ §®à®¬ ¢¨â®ª ᯨࠫ¨ á®á⮨⠨§ ¤¢ãå ¯àï¬ëå,
¯ à ««¥«ì­ëå ®á¨  , ¨ ¤¢ãå ªà¨¢®«¨­¥©­ëå ãç áâ-
ª®¢. àאַ«¨­¥©­ë¥ ãç á⪨ ᮮ⢥âáâ¢ãîâ ¤¢¨-
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à®áâì ®áâ ¥âáï ­¥¨§¬¥­­®©.
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„«ï ⮣®, çâ®¡ë ®æ¥­¨âì ¢«¨ï­¨¥ ¤¨ ¬¥âà  ª -
¢¨â â®à  ¨ § §®à  ¢ 墮á⥠­  ¯®¢¥¤¥­¨¥ ¬®¤¥«¨,
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à §  ¯à¥¢®á室¨« ¬¨­¨¬ «ì­ë©, ®áâ «ì­ë¥ ¨¬¥«¨
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à  ¢¥¤¥â ª 㢥«¨ç¥­¨î  ¬¯«¨âã¤ë ª®«¥¡ ­¨© ¨
(¢ ¬¥­ì襩 á⥯¥­¨) ª 㬥­ì襭¨î ¨å ç áâ®âë.
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­¥áª®«ìª® à § ¯à¥¢®á室¨âì 㣫®¢ãî ᪮à®áâì ­ -
ç «ì­®£® ¢®§¬ã饭¨ï. à¨¬¥àë १ã«ìâ â®¢ à á-
ç¥â  ¯®ª § ­ë ­  à¨á. 6 { 7.
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á«ãç ¥ ¬®¤¥«¨ á ª®à¬®¢®©ç áâìî ¬ «®£® ¤¨ ¬¥âà 
(à¨á. 8 { 10).
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§ ¬ë¢ ç á⨠¬®¤¥«¨, à á¯®«®¦¥­­®© ¢¯¥à¥¤¨ 業-
âà  ¨­¥à樨. ‚§ ¨¬­®¥ ¯®«®¦¥­¨¥ ¬®¤¥«¨ ¨ ª -
¢¥à­ë ¢ ¬®¬¥­â, ¯à¥¤è¥áâ¢ãî騩 ¯®â¥à¥ ãá⮩-
稢®áâ¨, ¯®ª § ­® ­  à¨á. 11.
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(50 ¤«¨­).
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ᨬ¬¥âà¨ç­ë ®â­®á¨â¥«ì­® «¨­¨¨  = 0. ‚ í⮬
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¢¯ ¤ ¥â á ­ ¯à ¢«¥­¨¥¬, § ¤ ­­ë¬ ¯à¨ áâ àâ¥.
à¨ ¬ «ëå § §®à å ç áâ® ­ ¡«î¤ ¥âáï § ¬¥â-
­ ï  á¨¬¬¥âà¨ï (à¨á. 12, 13). ‚ í⮬ á«ãç ¥ ¢®§-
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¢®©âà ¥ªâ®à¨¨ ­ ª« ¤ë¢ îâáﮤ¨­ ­ ¤à㣮©, ­®
¨á. 8. ¥ãá⮩稢®¥ ¤¢¨¦¥­¨¥ ¬®¤¥«¨ ¢ ª ¢¥à­¥.
Š®®à¤¨­ â  業âà  ¨­¥à樨
¨á. 9. ¥ãá⮩稢®¥ ¤¢¨¦¥­¨¥ ¬®¤¥«¨ ¢ ª ¢¥à­¥.
“£®« â ­£ ¦  ¨ 㣫®¢ ï ᪮à®áâì
業âà ª à⨭ë ᬥ饭 ®â­®á¨â¥«ì­® «¨­¨¨  = 0
(à¨á. 12). ‚ ¤à㣨å á«ãç ïå ¯®á«¥¤®¢ â¥«ì­ë¥
¢¨âª¨ á¬¥é¥­ë ¤à㣠®â­®á¨â¥«ì­® ¤à㣠, ¨ 業âà
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‚á«¥¤á⢨¥ í⮣® ¬®¤¥«ì ®âª«®­ï¥âáï ®â ¯¥à¢®-
­ ç «ì­® § ¤ ­­®© âà ¥ªâ®à¨¨ (à¨á. 14).
’ ª¨¬ ®¡à §®¬, à §¬¥à ª ¢¨â â®à  ®ª §ë¢ ¥â
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­¥© ç á⨠¬®¤¥«¨.
Žâ¬¥ç¥­® â ª¦¥, çâ® ¬ «ë¥ ¨§¬¥­¥­¨ï ä®à¬ë
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ïâì ­  ¯®¢¥¤¥­¨¥ ¬®¤¥«¨.
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72 ‘. ˆ. ã⨫¨­
ISSN 1561-9087 à¨ª« ¤­  £÷¤à®¬¥å ­÷ª . 2000. ’®¬ 2 (74), N 3. ‘. 65{74
¨á. 10. ¥ãá⮩稢®¥ ¤¢¨¦¥­¨¥ ¬®¤¥«¨ ¢ ª ¢¥à­¥.
“£®« â ­£ ¦  ¨ 㣫®¢ ï ᪮à®áâì
¨á. 11. ¥ãá⮩稢®¥ ¤¢¨¦¥­¨¥ ¬®¤¥«¨.
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¢ ª®à¬®¢®© ç áâ¨.  áç¥âë ¯®ª § «¨, çâ® ¬®¤¥«ì
á 㣫®¬ ­ ª«®­  ¯®¢¥àå­®á⨠®ª®«® 1
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襭­ë¬, â ª ¨ á 㢥«¨ç¥­­ë¬ ª ¢¨â â®à®¬.
¨á. 12. €á¨¬¬¥âà¨ç­®¥ ¤¢¨¦¥­¨¥ ¬®¤¥«¨ ¢ ª ¢¥à­¥.
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¨á. 13. €á¨¬¬¥âà¨ç­®¥ ¤¢¨¦¥­¨¥ ¬®¤¥«¨.
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Œ®¤¥«ì, à ¤¨ãá ª®à¬ë ª®â®à®© 㢥«¨ç¥­ ­  15%
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ª®ç áâ®â­®© á®áâ ¢«ïî饩 㣫®¢ëå ª®«¥¡ ­¨©,
ª ª ­  à¨á. 15, «¨¡® á®áâ ¢«ïî饩, ¬®­®â®­­®
¢®§à áâ î饩 á® ¢à¥¬¥­¥¬. ‚ ®¡®¨å á«ãç ïå ¬®-
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‘. ˆ. ã⨫¨­ 73
ISSN 1561-9087 à¨ª« ¤­  £÷¤à®¬¥å ­÷ª . 2000. ’®¬ 2 (74), N 3. ‘. 65{74
¨á. 14. €á¨¬¬¥âà¨ç­®¥ ¤¢¨¦¥­¨¥ ¬®¤¥«¨.
Š®®à¤¨­ â  ¨ ¢¥à⨪ «ì­ ï ᪮à®áâì 業âà  ¨­¥à樨
¨ 㣮« â ­£ ¦ 
¨á. 15. ¥à¥£ã«ïà­®¥ ¤¢¨¦¥­¨¥ ¬®¤¥«¨.
“£®« â ­£ ¦ 
(à¨á. 16).
€­ «¨§ ¯®«ã祭­ëå १ã«ìâ â®¢ ¯®§¢®«ï¥â ᤥ-
« âì ¢ë¢®¤, çâ® ¤¢¨¦¥­¨¥ ¬®¤¥«¨ á ª ¢¨â â®à®¬,
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ᮡ®© ãáâ®©ç¨¢ë¥ ª®«¥¡ ­¨ï á ¯®áâ®ï­­ë¬¨  ¬-
¨á. 16. ¥à¥£ã«ïà­®¥ ¤¢¨¦¥­¨¥ ¬®¤¥«¨.
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â â®à  ¤¢¨¦¥­¨¥ ¬®¦¥â ¡ëâì «¨¡®  ¯¥à¨®¤¨ç¥áª¨
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â â ­ «®¦¥­¨ï ª®«¥¡ ­¨© á à §«¨ç­®© ç áâ®â®© ¨
­®á¨âì ­¥à¥£ã«ïà­ë© å à ªâ¥à.
1. ‹®£¢¨­®¢¨ç ƒ.‚. ƒ¨¤à®¤¨­ ¬¨ª  â¥ç¥­¨© ᮠ᢮-
¡®¤­ë¬¨ £à ­¨æ ¬¨.{ Š¨¥¢:  ãª. ¤ã¬ª , 1969.{
208 á.
2. ‘¥à¥¡à类¢ ‚.‚. ¥ª®â®àë¥ § ª®­®¬¥à­®á⨠à á-
è¨à¥­¨ï á¥ç¥­¨© ®á¥á¨¬¬¥âà¨ç­®© ¨ áä¥à¨ç¥áª®©
ª ¢¥à­ // ƒ¨¤à®¬¥å ­¨ª .{ ‚ë¯. 62.{ 1990.{ ‘. 80-
88.
3. Putilin S.I. Stability of supercavitating Slender Body
During Water Entry and Underwater motion //
AGARD.{ Report 827.{ 1998.{ ‘. 24-30.
4. ‹ãª®¬áª¨© ž.€., —ã£ã­®¢ ‚.‘. “¯à ¢«¥­¨¥ ¬®à-
᪨¬¨ ¯®¤¢¨¦­ë¬¨ ®¡ê¥ªâ ¬¨.{ ‹: ‘㤮áâ஥­¨¥,
1988.{ 271 á.
5. ‹®£¢¨­®¢¨ç ƒ.‚. ¥ª®â®àë¥ ¢®¯à®áë £«¨áá¨à®¢ -
­¨ï ¨ ª ¢¨â æ¨¨ // ’àã¤ë –€ƒˆ.{ ‚ë¯. 2052.{
1980.{ ‘. 3 {12.
6. ”¥é¥­ª® ‘.”. ¨ ¤à. €á¨¬¯â®â¨ç¥áª¨¥ ¬¥â®¤ë ¢
⥮ਨ «¨­¥©­ëå ¤¨ää¥à¥­æ¨ «ì­ëå ãà ¢­¥­¨© á
®âª«®­ïî騬áï  à£ã¬¥­â®¬.{ Š¨¥¢:  ãª. ¤ã¬ª ,
1981.{ 293 á.
7. Œ®¨á¥¥¢ .. €á¨¬¯â®â¨ç¥áª¨¥ ¬¥â®¤ë ­¥«¨­¥©-
­®© ¬¥å ­¨ª¨.{ Œ:  ãª  ”Œ, 1981.{ 400 á.
74 ‘. ˆ. ã⨫¨­