12
IAOe?IIAEUeIA AEAAeAI?ss IAOE OE?A?IE
?INOEOOO I?EEEAAeII? IAOAIAOEEE ? IAOAI?EE
*AAAIIA Aeieo?i Ieaenaiae?iae/
OAeE 531.38
IIA? EEANE ?OO?A
NENOAI A??INEII?A EAA?AIAEA
01.02.01 — oai?aoe/ia iaoai?ea
AAOI?AOA?AO
aeena?oaoe?? ia caeiaoooy iaoeiaiai nooiaiy
eaiaeeaeaoa o?ceei-iaoaiaoe/ieo iaoe
Aeiiaoeuee — 1998
Aeena?oaoeth ?oeiien.
?iaioa aeeiiaia a inoeooo i?eeeaaeii iaoaiaoeee iaoaiee IAI Oe?aie,
i.Aeiiaoeuee.
Iaoeiaee ea?aiee:/eai-ei?. IAI Oe?a?ie, aeieoi? o?c.-iao. iaoe,
i?ioani? Naa/aiei Ieaen?e sseiae/,
Aea?aeaaia iiaeaoeiaa aaei?i?no?aoe?y Oe?a?ie,
canooiiee aieiae
Iooeei iiiiaioe:
/eai-ei?. IAI Oe?a?ie, aeieoi? o?c.-iao. iaoe, i?ioani? Oa?eaiia Iaaei
Aaneeueiae/, ?inoeooo i?eeeaaeii? iaoaiaoeee ? iaoai?ee IAI Oe?a?ie,
caa. a?aeae?eii i?eeeaaeii? iaoai?ee;
eaiaeeaeao o?c.-iao. iaoe, aeioeaio Eiaaeue Aeeoi? ?aaiiae/, Aeiiaanueea
aea?aeaaia aeaaeai?y aoae?aieoeoaa oa a?o?oaeoo?e, aeioeaio eaoaae?e
aeui? iaoaiaoeee
I?iaaeia onoaiiaa:
?inoeooo iaoaiaoeee IAI Oe?a?ie, i. Ee?a, a?aeae?e aeeiai?ee ? no?eeino?
aaaaoiaei??ieo nenoai
Caoeno aaeaoaeaoueny “ 20 ” n?/iy 1999 ?. i 1500 aiaeei ia
canaeaii niaoeaeciaaii a/aii ?aaee Ae 11.193.01 i?e inoeooo i?eeeaaeii
iaoaiaoeee iaoaiee IAI Oe?aie ca aae?anith: 340114, i. Aeiiaoeuee,
aoe. ?. Ethenaiao?a, 74.
C aeena?oaoeth iiaeia iciaeiieoenue o iaoeia?e aaeioaoe inoeoooo
i?eeeaaeii iaoaiaoeee iaoaiee IAI Oe?aie ca aae?anith: 340114,
i.Aeiiaoeuee, aoe. ?. Ethenaiao?a, 74
Aaoi?aoa?ao ?icneaiee “ 17 “ a?oaeiy 1998 ?.
A/aiee nae?aoa?
niaoeaeciaaii a/aii ?aaee
A.?. Ia?eianueeee
CAAAEUeIA OA?AEOA?ENOEEA ?IAIOE
Aeooaeueinoue oaie. Aeeiai?ea nenoai ca’ycaieo oaa?aeeo o?e (NCOO) ?
iaeiei ?c ?icae?e?a aiae?oe/ii? iaoai?ee, yeee iaea?eueo ei?enoo?oueny
iiieoii o oaia??oi?e /an. ?ioa?an aei nenoai aaniethoii oaa?aeeo o?e,
ca’ycaieo i?ae niaith ??cieie oeiaie c’?aeiaiue c aieiiiiieie ?
iaaieiiiiieie, noaoe?iia?ieie ? ianoaoe?iia?ieie a’ycyie, aeeeeeaiee
oe?ieei aeei?enoaiiyi oe??? iaoaiaoe/ii? iiaeae? i?e ?icaeyaeaii?
aaeeei? e?eueeino? ??ciiiai?oieo caaea/ iaoai?ee aeeaeo i?aai?ci?a,
iaaeeai? i?e?iaee oa no/anii? oaoi?ee. Cie?aia, oea noino?oueny
iaa?aaoe?eieo i?eeaae?a, a??inoao?a, iai?ioeyoi??a, oeaio?eooa, o?e, ui
iaa?oathoueny ia no?oi? aai no?oiiiio i?aea?n?. Iiaeaeue NCOO c oni?oii
aeei?enoiao?oueny aeey ?ica’ycaiiy neeaaeieo caaea/ aeeiai?ee eini?/ieo
aia?ao?a, iai?eeeaae, noiooiee?a c iiaea?eiei iaa?oaiiyi oa ?ooiieie
aeaiaioaie.
A?aeiinii iauiaeaaii aoei aeyaeaii ua iaeei aniaeo i?eeeaaeiiai
aeei?enoaiiy NCOO, iia’ycaiee c aeine?aeaeaiiyi aeeiai?/ieo aeanoeainoae
noa?aeiueiaeo nenoai, ui iiaeaeththoue oae? oaoi?/i? ia’?eoe, ye ?aeaoe,
aaee, ui iaa?oathoueny, e?iaoe/i? cae?a/? aia?a?? oa ?io?. Aeei?enoaiiy
iiaeo iaoa??ae?a, ye? aeiioneathoue cia/i? i?iaeie, aeey eiino?othaaiiy
no/anieo oaoi?/ieo i?eeaae?a i?ecaaei aei iaiao?aeiino? o?aooaaiiy ?o
i?oaeieo aeanoeainoae. Caaea/?, ui ?ai?oa ?ica’ycoaaeeny c aeei?enoaiiyi
iiaeae? aaniethoii oaa?aeiai o?ea, ca?ac iio?aaothoue ?ioi?, a?eueo
aio/ei? o?ce/ii? iinoaiiaee iiaeae? ia’?eoa, yea a?aoiao? eooia?
ia?ai?uaiiy eiai neeaaeiaeo /anoei, ine?eueee iia? aeanoeaino?
iaoa??ae?a noaee /eieoe ?noioiee aieea ia eiai ?oo. Iaeiei c i?eeiyoieo
niinia?a o?aooaaiiy iiaeaoeeaino? oaeeo ia’?eo?a aeyaey?oueny ?o
iiaeaethaaiiy ca aeiiiiiaith NCOO. Cai?ia nenoai c ?iciiae?eaieie
ia?aiao?aie, aiae?c aeeiai?/ieo aeanoeainoae yeeo c?iaeoe aeoaea aaaeei
/a?ac neeaaei?noue ?o iaoaiaoe/iiai iieno, nenoaiaie oaa?aeeo o?e,
aeicaiey? c aeinoaoiueith oi/i?noth aecia/eoe an? iaiao?aei?
oa?aeoa?enoeee nenoai, ui aeine?aeaeothoueny.
I?aeoe/ia cia/aiiy NCOO aecia/a? ieceo aeooaeueieo iaoeiaeo iai?yie?a.
Na?aae ieo oeaio?aeueia i?noea caeia? caaea/a i?i ?oo NCOO c ia?ooiiith
oi/eith. Caaea/a i?i ?oo iaa?oue aeaio ca’ycaieo oaa?aeeo o?e
aeyaey?oueny cia/ii neeaaei?oith a?ae a?eueo i?ae aeaionio??/ii?
eeane/ii? caaea/? i?i ?oo aaaeeiai oaa?aeiai o?ea iaaeiei ia?ooiii?
oi/ee. Iaeiae, aaea?oueny c oni?oii ?ica’ycoaaoe caaea/?, iia’ycai? c
aea/aiiyi ?oo?a ia’?eo?a, ui iiaeaeththoueny NCOO. ?ica’ycaiiy oeeo
caaea/ ii?aeiaii c oaeeie i??caeuaie, ye I.I. Aiaiyaeainueeee, E.
A?ooaiao?a, I.TH. ?oe?inueeee, Ae.I. Ee?iia, A.I. Eioeyeia, Ae.I.
Ia?e?i, I.TH. Ean?ia, E. E?eia, I.?. Eo?’?, A.A. ?oiyioeaa, I.ss.
Naa/aiei, A.A. Noi?iaeaiei, I.?. Oai/aiei, I.A. Oa?eaiia, I.A. *aoa?a oa
?i.
I?e ?icaeyae? caaea/ i?i ?oo NCOO aeine?aeieee iaiaaathoueny aeey
ni?iuaiiy aiae?co iiai?noth aeei?enoiaoaaoe niaoeeo?/i? iniaeeaino?
ia’?eo?a, ui aea/athoueny, oa ?aaeei?a ?o ?iaioe. O oeueiio ca’yceo
iaeiei c iai?yie?a ?icaeoeo oai??? NCOO ? iiooe iaea?eueo ?aoe?iiaeueieo
oi?i ??aiyiue ?ooo NCOO, i?enoiniaaieo aei iiaiiai aiae?co
oa?aeoa?enoee iiaeae?.
Ianooiiei aaaeeeaei e?ieii aeine?aeaeaiue ? ciaoiaeaeaiiy oi/ieo
?ica’yce?a io?eiaieo ??aiyiue. Iiaoaeiaa oi/ieo ?ica’yce?a ??aiyiue ?ooo
NCOO ? neeaaeiith /a?ac aenieee ii?yaeie nenoaie aeeoa?aioe?aeueieo
??aiyiue, a?aenooi?noue a?aeiia?aeiiai iaoaiaoe/iiai aia?aoo oa
aoaeoeaieo iaoiae?a, ui aeicaieythoue ciaeoe ?ica’ycee a yaiiio
aeaeyae?. Oiio nooo?aeo ?acoeueoao?a a oe?e iaeano? ia oae aaaaoi.
Aieiaiei /eiii aiie iia’ycai? c iiaoaeiaith noaoe?iia?ieo ?ica’yce?a, ui
iathoue aaaeeeaa i?eeeaaeia cia/aiiy, aai c iiaoaeiaith ?ica’yce?a
nenoai aeaio oaa?aeeo o?e niaoe?aeueiiai aeaeyaeo oa c’?aeiaiiy. A
oeueiio ca’yceo aeooaeueiei i?aaenoaaey?oueny iiooe iiaeo eean?a oi/ieo
?ica’yce?a nenoai n ca’ycaieo oaa?aeeo o?e, ine?eueee aiie ni?iiiaei?
c?iaeoe a?eueo c?icoi?eeie oa?aeoa?i? iniaeeaino? iiaaae?iee iiaeae? a
oe?eiio (iai?eeeaae, aeey iiaeaeae noa?aeiueiaeo eiino?oeoe?e) oa
iiaeooue iineoaeeoe o yeino? ii?iaeieo aeey aeine?aeaeaiiy ?ooo
iaoai?/ii? nenoaie a ?o ieie?.
Ca’ycie ?iaioe c iaoeiaeie i?ia?aiaie, ieaiaie, oaiaie. Aeine?aeaeaiiy
ii aeena?oaoe?? i?iaiaeeeenue ca?aeii c Ieaiaie iaoeiaeo aeine?aeaeaiue
aiaeaeie?a i?eeeaaeii? oa oaoi?/ii? iaoai?ee ?inoeoooo i?eeeaaeii?
iaoaiaoeee ? iaoai?ee IAI Oe?a?ie: ia 1990 — 1995 ?iee ii
aea?aeathaeaeaoi?e oai? — 01900018561 — “?ic?iaea iaoaiaoe/ieo iiaeaeae
neeaaeieo iaoai?/ieo nenoai ? iaoiae?a ?o aeine?aeaeaiiy ?c
canoinoaaiiyi aei caaea/ iaoeiiaoaeoaaiiy” oa ia 1996 — 2000 ?iee ii
aea?aeathaeaeaoi?e oai? — 0196U002837 — “Iaoaiaoe/i? iaoiaee
eiino?oeoeaiiai aeine?aeaeaiiy no/anieo i?iaeai no?eeino?, ea?oaaiiy oa
aeeiai?ee aca?iiae?th/eo o?e”, ye? aeeiioaaeeny a?aeiia?aeii aei
iinoaiia I?aceae?? IAI Oe?a?ie; a oaeiae o 1997 — 1998 ?ieao o ?aieao
i?iaeoo 1.4/155 “Iaoaiaoe/i? iaoiaee eiino?oeoeaiiai aeine?aeaeaiiy
no/anieo i?iaeai aeeiai?ee NCOO” Aea?aeaaiiai oiiaeo ooiaeaiaioaeueieo
aeine?aeaeaiue I?i?noa?noaa Oe?a?ie o ni?aaao iaoee oa oaoiieia?e.
Iaoa ? caaea/? aeine?aeaeaiiy. Iaoith ?iaioe iiaoaeiaa iiaeo eean?a
oi/ieo ?ica’yce?a caaea/ i?i ?oo nenoai n a??ineii?a Eaa?aiaea
iaa?eueiiai oa iai?acaieiaiiai oei?a.
Aeey aeinyaiaiiy iaoe ae?oothoueny ianooii caaea/:
1) aea?? ci?iieo, ye? iienothoue iieiaeaiiy aeine?aeaeoaaieo iaoai?/ieo
ia’?eo?a o ?ia?oe?aeueiiio i?inoi??; iaea?aeaiiy ??aiyiue ?ooo ia’?eo?a
o oaeeo ci?iieo;
2) ciaoiaeaeaiiy oa aeine?aeaeaiiy oiia ?nioaaiiy caaeaieo eean?a oi/ieo
?ica’yce?a oeeo aeeoa?aioe?aeueieo ??aiyiue;
3) ciaoiaeaeaiiy caeaaeiino? ci?iieo caaea/? a?ae /ano.
Iaoeiaa iiaecia iaea?aeaieo ?acoeueoaoia aecia/a?oueny ianooiieie
iieiaeaiiyie:
1) Aia?oa io?eiaii ??aiyiiy ?ooo iaa?eueii? nenoaie n aaaeeeo a??ineii?a
Eaa?aiaea wmetafile8? ??u???????????
???????????yyy????.????1?????????????
A???&??yyyy?????Ay¤y?D???&??MathType??p????uiya?????2)
Iiaoaeiaaii iiaee eean oi/ieo ?ica’yce?a oaeeo ??aiyiue. Eiio
a?aeiia?aeathoue ?ooe ca’ycee a??ineii?a, i?e yeeo a?n? neiao??? on?o
o?e nenoaie caeeoathoueny a iaei?e aa?oeeaeuei?e ieiuei?; aei oiai ae
a?n? a??ineii?a c ?iaeaenaie ?c i?aeiiiaeeie M a?aeoeeai? ii ??ci? aiee
a?ae aa?oeeae?, caa??aath/e ??aieie eooe iooaoe??, a a?n? o?e c
?iaeaenaie ?c i?aeiiiaeeie K eie?iaa?i? o aanue /an ?ooo aaeoi?o
aa?oeeae?. Cacia/aiee eean ocaaaeueith? a?eueoo e?euee?noue a?aeiieo ia
oeae /an ianoaoe?iia?ieo ?ica’yce?a caaea/? i?i ?oo iaa?eueii? nenoaie
a??ineii?a Eaa?aiaea. Cie?aia, a?i i?noeoue o nia? caaea/o i?i ?nioaaiiy
iiae?aieo ?oo?a, yea io?eio?oueny c aeaii? i?e M=N, a oaeiae caaea/o
i?i ??aiii??i? iaa?oaiiy nenoaie a??ineii?a iaaeiei aa?oeeae?, yea
aeieeaa? c aeaii? i?e wmetafile8? ??U????????????
???????????yyy????.????1??????????????
???&??yyyy?????Ayaya`???&??MathType?? ????u?th??????3)
Aia?oa iaea?aeaii iaiao?aei? oiiae ?nioaaiiy ?oo?a oe??? iaoai?/ii?
nenoaie, i?e yeeo a?n? neiao??? a??ineii?a c ?iaeaenaie ?c i?aeiiiaeeie
K eie?iaa?i? o aanue /an ?ooo aaeoi?o aa?oeeae?, a o?ea c ?iaeaenaie ?c
i?aeiiiaeeie M ?ooathoueny aeia?eueii.
4) Iiaoaeiaaii iiaee eean oi/ieo ?ica’yce?a ??aiyiue ?ooo nenoaie n
aaaeeeo a??ineii?a Eaa?aiaea iai?acaieiaiiai oeio. A?i iieno? ?ooe
oaei? nenoaie, i?e yeeo an? o?ea, e??i iaeiiai, ?ooathoueny iiae?aii
iaeia iaeiiio. Aea/ai? aeinoaoi? oiiae ?nioaaiiy oeeo ?oo?a. Caaea/o
caaaeaii aei eaaae?aoo?.
I?aeoe/ia cia/aiiy iaea?aeaieo ?acoeueoao?a. ?acoeueoaoe aeena?oaoe??
iathoue a iniiaiiio oai?aoe/iee oa?aeoa?. Aiie iiaeooue aooe aeei?enoaii
aeey c’ynoaaiiy oa?aeoa?o ?ooo iaoai?/ii? nenoaie a ieie? noaoe?iia?ieo
?oo?a, ye? i?noyoueny a ciaeaeaieo ?ica’yceao, aeey aeine?aeaeaiiy
a?eueo oe?ieiai eeano ?oo?a a ieie? io?eiaieo ?oo?a, a oaeiae aeey
aea/aiiy iioeo aeeiaii/ieo aeanoeainoae nenoai a??ineiiia Eaa?aiaea.
?acoeueoaoe aeena?oaoe?? i???ioiaai? ia ?o aeei?enoaiiy o iiaoaeia?
no/anieo oaoi?/ieo eiino?oeoe?e oa i?e ?ic?iaoe? iaoiae?a ?o ea?oaaiiy.
Ai?iaaoey ?acoeueoao?a aeena?oaoe??. Iniiai iaoeia ?acoeueoaoe
aeena?oaoeieii ?iaioe aeiiiaaeaeeny oa iaaiai?thaaeeny ia:
— I?aeia?iaei?e eiioa?aioe?? “Onoie/eainoue, oi?aaeaiea e aeeiaieea
oaa?aeiai oaea”, Aeiiaoeuee, 2-6 aa?aniy 1996 ?.;
— O?ao?e E?einuee?e I?aeia?iaei?e Iaoaiaoe/i?e oeie?, naeoe?y I “Iaoiae
ooieoeee Eyioiiaa e aai i?eeiaeaiey”, Aeoooa, 16-23 aa?aniy 1996 ?.;
— XXII Yugoslav Congress of Theoretical and Applied Mechanics, YUCTAM,
Vrnjacka Banja, Yugoslavia, 2-7 June 1997;
— I?aeia?iaei?e eiioa?aioe?? “Iaoaiaoeea a eiaeono?ee”,Oaaai?ia,29
/a?aiy—3 eeiiy 1998 ?.;
— International Congress of Mathematicians (ICM-98), Berlin, August
18-27, 1998;
— Nai?ia?ao aiaeaeie?a i?eeeaaeii? oa oaoi?/ii? iaoai?ee ?III IAI
Oe?a?ie (Aeiiaoeuee, ea?. /eai-ei?. IAI Oe?a?ie I.A. Oa?eaiia), 1994 —
1998.
Ioae?eaoe??. Ca oaiith aeena?oaoe iioaeeiaaii 6 ae?oeiaaieo i?aoeue, a
oiio /ene 3 a noaooyo iaoeiaeo aeo?iaea, 2 o iaoa?aeao iaeia?iaeieo
eiioa?aioee, 1 o ca?ieeo i?aoeue.
No?oeoo?a oa ianya aeena?oaoe??. Aeena?oaoeeia ?iaioa aeeeaaeaia ia 136
noi?ieao oa neeaaeaoueny c anooio, 4 ?icaeea, aeniiaea, nieneo
aeei?enoaieo aeaea?ae c 95 iaeiaioaaiue ia 10 noi?ieao oa aeiaeaoea ia
14 noi??ieao, i?noeoue a nia? 12 ?ethno?aoe?e.
INIIAIEE CI?NO
O anooi? iaa?oioiao?oueny aeooaeuei?noue aeaii? ?iaioe, oi?ioeth?oueny
iaoa ? iniiai? caaea/? aeine?aeaeaiue, aeeeaaeaoueny iaoeiaa iiaecia ?
i?aeoe/ia oeiinoue ?iaioe, iaaiaeyoueny a?aeiiino? i?i ai?iaaoe?th
?acoeueoao?a ?iaioe.
A ia?oiio ?icae?e? iiaea?oueny iaeyae ?ia?o, ye? iathoue a?aeiioaiiy
aei oaie aeena?oaoe??, ie?aneththoueny iniiai? aoaie ?icaeoeo iaoeiai?
aeoiee o oaeeo aaeocyo oai??? NCOO, ye iiooe ??cieo oi?i ??aiyiue ?ooo
NCOO oa ciaoiaeaeaiiy oi/ieo ?ica’yce?a caeiaooeo ??aiyiue.
Ai?iaaaeaeothoueny a ?icaeyae iaoai?/i? ia’?eoe, ye? aoaeooue aea/aoeny
o ianooiieo ?icae?eao aeena?oaoe??. ?icaeyaea?oueny nenoaia n aaaeeeo
a??ineii?a Eaa?aiaea wmetafile8? ??S???????????
???????????yyy????.????1?????????????
?a???&??yyyy?????AyAy A???&?
?MathType??P????u?th??????I.ss. Naa/aiei oa I.TH. Ean?ia aia?oa
iiaoaeoaaee ianoaoe?iia?iee oi/iee ?ica’ycie ??aiyiue ?ooo iaa?eueii?
nenoaie n a??ineii?a Eaa?aiaea. Eiio a?aeiia?aeathoue ?ooe nenoaie, i?e
yeeo eooe iooaoe?? oa i?aoean??, ui aecia/athoue iieiaeaiiy inae
neiao??? o?e a ?ia?oe?aeueiiio i?inoi??, iaeiaeia?. Oiio a?n? on?o
a??ineii?a iaeaaeaoue aei iaei??? i?yii?, a nenoaia a oe?eiio ?ooa?oueny
ye iaeia oaa?aea o?ei c oith eeoa ??cieoeath, ui eiaeai a??ineii
iaa?oa?oueny iaaeiei nai?? in? neiao??? c? nai?th eooiaith oaeaee?noth.
I?ci?oa I.A. Oa?eaiia onoaiiaea ?nioaaiiy a?eueo caaaeueiiai eeano
?oo?a, eiee a?n? neiao??? a??ineii?a caeeoathoueny a iaei?e
aa?oeeaeuei?e ieiuei?, aea o caaaeueiiio aeiaaeeo a?aeoeeythoueny ii
??ci? aiee a?ae aa?oeeae? oae, uia eooe iooaoe?? on?o o?e aoee ??aieie
i?ae niaith ? a?aei?iieie a?ae ioey. O?ea nenoaie ?ooathoueny i?e
oeueiio iiae?aii iaeia iaeiiio. O oaeiio ?ac? iica eieii ?icaeyaeo
caeeoeeenue aeiaaeee, eiee eooe iooaoe?? aeayeeo o?e nenoaie
aei??aiththoue ioeth. Oe? aeiaaeee, a oaeiae ieoaiiy uiaei ?nioaaiiy
?oo?a nenoai iai?acaieiaiiai oeio, ye? ocaaaeueiththoue iiae?ai? ?ooe, ?
aea/ai? o oe?e aeena?oaoe??.
A ae?oaiio ?icae?e? aeeeaaeaii caaaeueio iaoiaeeeo aeena?oaoe?eieo
aeine?aeaeaiue, yea neeaaea?oueny c o?aaeeoe?eieo caoiae?a aiae?oe/ii?
aeeiai?e? ciaoiaeaeaiiy oi/ieo ?ica’yce?a ??aiyiue ?ooo iaoai?/ieo
ia’?eo?a.
I?ney ?aoe?iiaeueiiai aeai?o ci?iieo, ye? iienothoue iieiaeaiiy
iaoai?/ii? nenoaie, ui aea/a?oueny, a?aeiinii ?ia?oe?aeueiiai i?inoi?o,
caienothoue o oeeo ci?iieo ??aiyiiy ?ooo ia’?eoo, ui aeine?aeaeo?oueny.
Aeae? ?aaeei ?ooo iaoai?/ii? nenoaie, yeee iathoue iai?? ciaeoe,
iienothoue iaoaiaoe/ieie iaoiaeaie. A ?acoeueoao? aeieeathoue
caeaaeiino?, ye? ca’ycothoue i?ae niaith iaa?aeii? aaee/eie, ui
aoiaeyoue aei ??aiyiue ?ooo oe??? nenoaie. Oaeei /eiii, iaoai?/io
caaea/o i?i anoaiiaeaiiy ??cieo oei?a ?oo?a ia’?eoo, ui ?ooa?oueny,
caaaeaii aei iaoaiaoe/ii? caaea/? i?i ?nioaaiiy o nenoaie
aeeoa?aioe?aeueieo ??aiyiue oi/ieo ?ica’yce?a c a?aeiiith no?oeoo?ith.
Aeey ?ica’ycaiiy inoaiiuei? caaea/? aeei?enoaii iai?aiaa?iaiee iaoiae,
yeee iieyaa? o ianooiiiio. sseui ?c ni?aa?aeiioaiue, ui caaeathoue
no?oeoo?o ?ica’yceo, iiaeeeai ae?aceoe aeaye? iaa?aeii?, oi ?o
aeeeth/athoue ?c nenoaie ??aiyiue ?ooo iaoai?/iiai ia’?eoo. Oiae? oey
nenoaia noa? ia?aicia/aiiith. O ?ac?, eiee iiaeooue aooe ciaeaeai?
oiiae noi?niino? io?eiaii? ia?aicia/aii? nenoaie oa aeiaaaeaia
iiaeeea?noue ?o ?ica’ycaiiy, oi, c iaeiiai aieo, i?ney ?ioaa?oaaiiy
nenoaie aeeoa?aioe?aeueieo ??aiyiue, ui io?eio?oueny o aeaiiio aeiaaeeo,
ciaoiaeyoueny caeaaeiino? ci?iieo caaea/? a?ae /ano, a, c ae?oaiai aieo,
i?e ?ica’ycaii? iaea?aeaieo oiia ?nioaaiiy ?ica’yce?a, ye? aea/athoueny,
anoaiiaeththoueny iaiaaeaiiy ia iaoai?/i? ia?aiao?e, ui oa?aeoa?ecothoue
?iciiae?e ian o o?eao, niiniae ?o c’?aeiaiiy oa eiio?ao?aoe?th nenoaie
a??ineii?a.
Aei iaaeie?e?a iai?aiaa?iaiiai iaoiaeo o?aaa a?aeianoe a?aenooi?noue
oi?aa?naeueieo oa aoaeoeaieo iaoiae?a ciaoiaeaeaiiy oiia noi?niino?
ia?aicia/aieo nenoai aeeoa?aioe?aeueieo ??aiyiue. Oiio aeoaea aaaeeeai
aaeaei ia?aoe ci?ii? caaea/?, uia no?oeoo?a ?ica’yceo, yeee aea/a?oueny,
i?eeiyea iaea?eueo i?inoee aeaeyae, a ia?aicia/aia nenoaia aeyaeeanue
aeinooiiith aei aeine?aeaeaiiy, ui aeicaieeei a ciaeoe oiiae ??
noi?niino?.
Aeeeaaeaia iaoiaeeea aoea aeei?enoaia I.A. Oa?eaiiaei i?e iiaoaeia?
oi/ieo ?ica’yce?a caaea/? i?i iiae?ai? ?ooe iaa?eueii? nenoaie
a??ineii?a Eaa?aiaea. Aiia canoiniao?oueny a ianooiieo ?icae?eao
aeena?oaoe?? aeey ciaoiaeaeaiiy iiaeo eean?a ?ica’yce?a ??aiyiue ?ooo
nenoai a??ineii?a Eaa?aiaea.
A ?icae?e? 3 aeiaaaeaii, ui nenoaia aaaeeeo a??ineii?a Eaa?aiaea
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nenoaie, i?e yeeo a?n? neiao??? o?e c ?iaeaenaie ?c i?aeiiiaeeie K
eie?iaa?i? aei aaeoi?a aa?oeeae?, a ?io? a??ineiie ?ooathoueny
aeia?eueii. C oeeo oiia aeieeaa?, ui o?ea wmetafile8?
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eie?iaa?i? aei aaeoi?a aa?oeeae?. I?ney i?aenoaiiaee (1) a ??aiyiiy ?ooo
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a?aeiinii ia?aiao??a, ye? caaeathoue ?iciiae?e ian o o?eao. I?e oeueiio
aeyaey?oueny, ui ia a?aei?io a?ae eeano iiae?aieo ?oo?a, noi?ni?noue
oiia (3) caeaaeeoue a?ae eiio?ao?aoe?? nenoaie o?e. Oae, ca’ycea
a??ineii?a, o yei? ?iaeaene iaeiiai aai e?eueeio ia?oeo (a?ae ia?ooiii?
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c’?aeiaiiy oa eiio?ao?aoe?th ca’ycee o?e.
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(3), ye? nooo?ai aeei?enoiaothoueny o ?icae?e? 3 aeey aeiaaaeaiiy
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wmetafile8? ??P?????????????
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A aeena?oaoe?ei?e ?iaio ca aeiiiiiaith eeane/ieo iaoiae?a aiae?oe/ii?
aeeiai?ee iiaoaeiaaii iia? eeane oi/ieo ?ica’yce?a ??aiyiue ?ooo nenoai
n aaaeeeo a??ineii?a Eaa?aiaea iaa?eueiiai oa iai?acaieiaiiai oei?a.
Aea/aii aeeiaii/i? aeanoeaino? ?oo?a nenoai, ui a?aeiia?aeathoue oeei
?ica’yceai. Io?eiai? ?acoeueoaoe iiaeooue aooe aeei?enoaii aeey
aeine?aeaeaiiy a?eueo oe?ieiai eeano ?oo?a a ?o ieie?.
A i?ioean? aeine?aeaeaiiy iaea?aeaii ianooii? iniiai? ?acoeueoaoe:
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Eaa?aiaea wmetafile8? ??u???????????
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a?aeiia?aeathoue ?ooe ca’ycee a??ineii?a, i?e yeeo a?n? neiao??? on?o
o?e nenoaie caeeoathoueny a iaei?e aa?oeeaeuei?e ieiuei?; aei oiai ae
a?n? ae?ineii?a c ?iaeaenaie ?c i?aeiiiaeeie M a?aeoeeai? ii ??ci? aiee
a?ae aa?oeeae?, caa??aath/e ??aieie eooe iooaoe??, a a?n? o?e c
?iaeaenaie ?c i?aeiiiaeeie K eie?iaa?i? o aanue /an ?ooo aaeoi?o
aa?oeeae?. Cacia/aiee eean ocaaaeueith? a?eueoo e?euee?noue a?aeiieo ia
oeae /an ianoaoe?iia?ieo ?ica’yce?a caaea/? i?i ?oo iaa?eueii? nenoaie
a??ineii?a Eaa?aiaea. Cie?aia, a?i i?noeoue o nia? caaea/o i?i ?nioaaiiy
iiae?aieo ?oo?a, yea io?eio?oueny c aeaii? i?e M=N, a oaeiae caaea/o i?i
??aiii??i? iaa?oaiiy nenoaie a??ineii?a iaaeiei aa?oeeae?, yea aeieeaa?
c aeaii? i?e wmetafile8? ??U????????????
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/ano.
Io?eiai? iaiaaeaiiy ia ia?aiao?e, ye? oa?aeoa?ecothoue ?iciiae?e ian a
o?eao, o aeiaaeeo, eiee niin?a c’?aeiaiiy ae?ineii?a caaeaii. Iaa?iaia
caaea/a — aecia/eoe iiaeeea? niiniae ii?aeiaiiy a??ineii?a, yeui
a?aeiiee ?o ?iciiae?e ian — ?ica’ycaia o aeiaaeeo o?ueio o?e. I?e
oeueiio aeyaey?oueny, ui ia a?aei?io a?ae eeano iiae?aieo ?oo?a
?nioaaiiy ?oo?a cacia/aiiai oeio caeaaeeoue a?ae eiio?ao?aoe?? nenoaie
o?e.
Iieacaii, ui a ?ac?, eiee a?n? o?e wmetafile8? ??’???????????
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i?e yeeo a?n? neiao??? ae?ineii?a c ?iaeaenaie ?c i?aeiiiaeeie K
eie?iaa?i? o aanue /an ?ooo aaeoi?o aa?oeeae?, a oaea c ?iaeaenaie ?c
i?aeiiiaeeie M ?ooathoueny aeia?eueii. C oeeo oiia aeieeaa?, ui o?ea
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ae?ineii?a Eaa?aiaea iai?acaieiaiiai oeio. Eiio a?aeiia?aeathoue ?ooe
nenoaie a??ineii?a, i?e yeeo eooe iooaoe?? on?o o?e, e??i aeayeiai
a??ineiia wmetafile8? ??Ue????????????
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?oo?a. Iieacaii ?o ?ica’yci?noue ca oiiae, ui o?aaa aecia/eoe ?iciiae?e
ian o o?eao, eiee caaeaii niin?a c’?aeiaiiy a??ineii?a. I?e oeueiio
anoaiiaeaii iaiaaeaiiy ia eiio?ao?aoe?th nenoaie: i?e ?ooao oeio (4),
(5) a?n? neiao??? o?e wmetafile8? ??’???????????
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NIENIE IIOAE?EIAAIEO I?AOeUe CA OAIITH AeENA?OAOe??
1.*aaaiia Ae.A. Ia iaeiii iaiauaiee caaea/e i iiaeiaiuo aeaeaeaieyo
nenoaiu ae?ineiiia Eaa?aiaea // Iaoaieea oaa?aeiai oaea. — 1995. —
Aui.27. — N.57-63.2.*aaaiia Ae.A. Ia iaeiii eeanna oi/iuo ?aoaiee
o?aaiaiee aeaeaeaiey nenoaiu n ae?ineiiia Eaa?aiaea // Aeiiiaiaei
Iaoeiiiaeueii? Aeaaeaii? Iaoe Oe?a?ie. — 1997. — ? 8. —
N.82-85.3.*aaaiia Ae.A. I iiaii eeanna aeaeaeaiee nenoaiu o?ao
ae?ineiiia Eaa?aiaea // Iaoaieea oaa?aeiai oaea. — 1997. — Aui.29. —
N.10-16.4.Chebanov D.A. About some classes of motions of Lagrange’s
gyroscopes system formed in a half-closed chain // Proceedings of the
XXII Yugoslav Congress of Theoretical and Applied Mechanics. — Belgrade
(Yugoslavia). — 1997. — P.57-60.5.*aaaiia Ae.A. Ia iaeiii eeanna
aeaeaeaiee nenoaiu ae?ineiiia Eaa?aiaea // O?oaeu Iaaeaeoia?. eiio.
“Iaoaiaoeea a eiaeono?ee”. — Oaaai?ia: Ecae-ai Oaaai?. ain. iaae. ei-oa.
— 1998. — N. 327-329.6.*aaaiia Ae.A. I iaeioi?uo /anoiuo aeaeaeaieyo
nenoaiu n naycaiiuo oyaeaeuo ae?ineiiia Eaa?aiaea // Nai?iee o?oaeia
iiaaaeeoaeae eiieo?na nooaeai/aneeo ?aaio a iaeanoe iaoaiaoeee, iaoaieee
e eeaa?iaoeee. — Aeiiaoee: 1993. — N. 22-33. (I?ai?./ AI Oe?aeiu. Ei-o
i?eee. iaoaiaoeee e iaoaieee; ? 93.03).
AIIOAOe?ss
*aaaiia Ae.I. Iia? eeane ?oo?a nenoai a??ineii?a Eaa?aiaea. — ?oeiien.
Aeena?oaoe?y ia caeiaoooy iaoeiaiai nooiaiy eaiaeeaeaoa
o?ceei-iaoaiaoe/ieo iaoe ca niaoe?aeueinoth 01.02.01 — oai?aoe/ia
iaoai?ea. — ?inoeooo i?eeeaaeii? iaoaiaoeee ? iaoai?ee IAI Oe?a?ie,
Aeiiaoeuee, 1998.
A aeena?oaoe?? iiaoaeiaaii oi/i? ?ica’ycee ??aiyiue ?ooo nenoai aaaeeeo
a??ineii?a Eaa?aiaea iaa?eueiiai oa iai?acaieiaiiai oei?a. Ciaeaeaii
iia? aeaee ?oo?a, ye? ocaaaeueiththoue eean iiae?aieo ?oo?a, eiee a?n?
neiao??? an?o o?e caeeoathoueny a iaei?e aa?oeeaeuei?e ieiuei? ?
a?aeoeeythoueny a?ae aa?oeeae? ia ??ai? eooe. Aeey iaa?eueii? nenoaie
aea/aii aeiaaeie eie?iaa?iino? inae neiao??? aeayeeo o?e aaeoi?o
aa?oeeae?; aeey nenoaie iai?acaieiaiiai oeio aeine?aeaeaii ?ooe, i?e
yeeo on? o?ea, e??i iaeiiai, ?ooathoueny iiae?aii iaeia iaeiiio.
I?iaiae?ciaaii oiiae ?nioaaiiy oeeo ?oo?a. Anoaiiaeaii caeaaeiino?
aieiaieo ci?iieo caaea/? a?ae /ano.
Eeth/ia neiaa: a??ineii Eaa?aiaea, oi/iee ?ica’ycie, iiae?ai? ?ooe,
iaa?eueia nenoaia, nenoaia iai?acaieiaiiai oeio.
*aaaiia Ae.A. Iiaua eeannu aeaeaeaiee nenoai ae?ineiiia Eaa?aiaea. —
?oeiienue.
Aeenna?oaoeey ia nieneaiea o/aiie noaiaie eaiaeeaeaoa
oeceei-iaoaiaoe/aneeo iaoe ii niaoeeaeueiinoe 01.02.01 — oai?aoe/aneay
iaoaieea. — Einoeooo i?eeeaaeiie iaoaiaoeee e iaoaieee IAI Oe?aeiu,
Aeiiaoee, 1998.
A aeenna?oaoeee iino?iaiu oi/iua ?aoaiey o?aaiaiee aeaeaeaiey nenoai
oyaeaeuo ae?ineiiia Eaa?aiaea ianaiaiaeiiai e iieocaieiooiai oeiia.
Iaeaeaiu iiaua aeaeu aeaeaeaiee, iaiauathuea eeann iiaeiaiuo aeaeaeaiee,
eiaaea ine neiiao?ee anao oae inoathony a iaeiie aa?oeeaeueiie ieineinoe
e ioeeiiaiu io aa?oeeaee ia ?aaiua oaeu. Aeey ianaiaiaeiie nenoaiu
eco/ai neo/ae eieeeiaa?iinoe inae neiiao?ee iaeioi?uo oae aaeoi?o
aa?oeeaee; aeey nenoaiu iieocaieiooiai oeia enneaaeiaaiu aeaeaeaiey, i?e
eioi?uo ana oaea, e?iia iaeiiai, aeaeaeoony iiaeiaii ae?oa ae?oao.
I?iaiaeece?iaaiu oneiaey nouanoaiaaiey oaeeo aeaeaeaiee. Onoaiiaeaiu
caaeneiinoe iniiaiuo ia?aiaiiuo caaea/e io a?aiaie.
Eeth/aaua neiaa: ae?ineii Eaa?aiaea, oi/iia ?aoaiea, iiaeiaiua
aeaeaeaiey, ianaiaiaeiay nenoaia, nenoaia iieocaieiooiai oeia.
Chebanov D.A. New classes of motions of Lagrange’s gyroscopes systems.
— Manuscript.
Thesis for a degree of Candidate of Sciences (Physics and Mathematics)
by speciality 01.02.01 — theoretical mechanics. — Institute of Applied
Mathematics and Mechanics of National Academy of Sciences of Ukraine,
Donetsk, 1998.
In the thesis there are constructed exact solutions of motion equations
of heavy Lagrange’s gyroscopes systems of nonfree and half-closed types.
New kinds of motions generalizing the class of similar motions when axes
of symmetry of all bodies remain in a vertical plane and they deviate at
equal angles from vertical are found. The case when axes of symmetry of
some bodies are collinear to the vector of vertical is studied for a
nonfree system. The motions in which all bodies, besides of one, perform
the similar motions are investigated for a system of half-closed type.
The conditions of existence of these motions are analyzed. The main
variables dependences from time are established.
Key words: Lagrange’s gyroscope, exact solution, similar motions,
nonfree system, system of half-closed type.
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