IAOe?IIAEUeIA AEAAeAI?ss IAOE OE?A?IE

?INOEOOO I?EEEAAeII? IAOAIAOEEE ? IAOAI?EE

AIEA?AANUeEA ??eia Ieaenaiae??aia

OAeE 531.38

AeINE?AeAEAIIss AeEIAI?*IEO AEANOEAINOAE

NENOAI CA’ssCAIEO OAA?AeEO O?E

? ?O CANOINOAAIIss AeI AEA*AIIss

AEANOEAINOAE NOA?AEIAAEO EIINO?OEOe?E

Niaoe?aeuei?noue 01.02.01 — oai?aoe/ia iaoai?ea

AAOI?AOA?AO

aeena?oaoe?? ia caeiaoooy iaoeiaiai nooiaiy

aeieoi?a o?ceei-iaoaiaoe/ieo iaoe

Aeiiaoeuee — 1999

Aeena?oaoe??th ? ?oeiien.

?iaioo aeeiiaii a ?inoeooo? i?eeeaaeii? iaoaiaoeee ? iaoai?ee IAI
Oe?a?ie, i.Aeiiaoeuee.

Io?oe?ei? iiiiaioe:

aeieoi? o?ceei-iaoaiaoe/ieo iaoe, i?ioani?

Aie/oe Inoai Ieeeiiae/,

Iaoe?iiaeueiee oaoi?/iee Oi?aa?neoao Oe?a?ie

(EI?), i.Ee?a, caa?aeoth/ee eaoaae?ith;

aeieoi? o?ceei-iaoaiaoe/ieo iaoe, i?ioani?

Ai?? Aaiiaae?e A?eoi?iae/,

Aeiiaoeueeee aea?aeaaiee oi?aa?neoao, i.Aeiiaoeuee

caa?aeoth/ee eaoaae?ith;

aeieoi? o?ceei-iaoaiaoe/ieo iaoe, i?ioani?

Eiaan Eaii?ae A?eai?iae/,

Ee?anueeee ?inoeooo cae?cie/iiai o?ainii?oo,

i.Ee?a, caa?aeoth/ee eaoaae?ith.

I?ia?aeia onoaiiaa: ?inoeooo iaoaiaoeee IAI Oe?a?ie, i. Ee?a,

a?aeae?e aeeiai?ee oa no?eeino?
aaaaoiaei??ieo nenoai.

Caoeno a?aeaoaeaoueny «_24__»__aa?aniy___ 1999 ?. i 15_ aiaeei? ia
can?aeaii? niaoe?ae?ciaaii? a/aii? ?aaee Ae 11.193.01 aeey caoenoo
aeena?oaoe?e ia caeiaoooy iaoeiaiai nooiaiy aeieoi?a o?ceei-iaoaiaoe/ieo
iaoe i?e ?inoeooo? i?eeeaaeii? iaoaiaoeee ? iaoai?ee IAI Oe?a?ie ca
aae?anith:

340114 i.Aeiiaoeuee, aoe. ?. Ethenaiao?a, 74.

C aeena?oaoe??th iiaeia iciaeiieoenue a a?ae?ioaoe? ?inoeoooo
i?eeeaaeii? iaoaiaoeee ? iaoai?ee IAI Oe?a?ie ca aae?anith:

340114 i.Aeiiaoeuee, aoe. ?. Ethenaiao?a, 74.

Aaoi?aoa?ao ?ic?neaii » 12″ na?iiy 1999 ?.

A/aiee nae?aoa?

niaoe?ae?ciaaii? a/aii? ?aaee
I.A. Eiaaeaanueeee

CAAAEUeIA OA?AEOA?ENOEEA ?IAIOE

Aeena?oaoe?eia ?iaioa i?enay/aia noai?aiith iaoaiaoe/ii( iiaeae?
i?oaeiiai ia’?eoo ia iniia? nenoaie ca’ycaieo oaa?aeeo o?e (NCOO),
niieo/aieo i?oaeieie oa?i??aie, iaa?oiooaaiith aaeaeaaoiino?
neii/aiiiii?ii? (NCOO) i iaia?a?aii? (i?oaeiee noa?aeaiue) iiaeaeae
i?oaeiiai ia’?eoo i aeine?aeaeaiith no?eeino? eiai ?iai/eo ?aaeei?a c
o?aooaaiiyi iaei? ianeiao?i? ia’?eoo.

Aeooaeuei?noue oaie. Inoaii?i /anii oaaao ana a?eueo oe?ieiai eiea
a/aieo i?eaa?oa? oaeee ia’?eo aiae?oe/ii? iaoai?ee, ye NCOO. Oea
iia’ycaii ye c i?eeeaaeieie, oae i c /enoi oai?aoe/ieie
aeine?aeaeaiiyie. ?ioa?an aei caaea/, a yeeo aeei?enoiao?oueny NCOO,
aeeeeeaiee aeaiia ianoaaeiaie:

1. Aaaaoi ia’?eo?a no/anii? oaoi?ee, cie?aia aa?aoe?eii?, ii?nueei? i
eini?/ii?, i?aaenoaaeythoue niaith nenoaie oa?i??ii c’?aeiaieo o?e.

2. Aeei?enoaiiy iiaeo iaoa??ae?a aeey aeaioiaeaiiy oaoi?/ieo i?eno?i?a
i?eaaei aei iiyae cia/ieo i?iaeiaiue, aeey a?aooaaiiy yeeo aeyaeeinue
iaiao?aeiei oei /e ?ioei iaoiaeii aaiaeeoe i?oaei?noue a cai?iiiiiaaio
iiaeaeue. Iaeiei c iiaeeeaeo i?aeoiae?a ?ica’ycaiiy oe??? i?iaeaie ?
aeei?enoaiiy a yeino? iiaeae? i?oaeiiai ia’?eoo nenoaie oaa?aeeo o?e,
ca’ycaieo i?oaeieie oa?i??aie.

I?eeeaaeaie NCOO iiaeooue neoaeeoe ai?inoao, a??ineii?/i? nenoaie, o?ea
ia no?oi? i no?oiiiio i?aea?n?, eie?ni? ae?iaae? i o.ii. Aea/aiith oaeeo
nenoai i?enay/ai? iiiia?ao?? i?ia?aeieo a/aieo: E. Aiooaiao?aa,
A.I. Coaiaa, I.TH.  Ioeiinueeiai, A.I. Eioeyeiaa, E.A. Eiaana, Ae.?.
Ia?eiia, I.ss. Naa/aiea oa ?i.

?yae aeooaeueieo i?eeeaaeieo caaea/ no/anii? oaoi?ee aeiaaa? ?ic?iaee
iaoiae?a aeine?aeaeaiiy no?eeino? noaoe?iia?ieo ?oo?a oaa?aeeo o?e, ui
iaa?oathoueny ia no?oi? aai no?oiiiio i?aea?n?. Aei oaeeo caaea/ iiaeia
a?aeianoe i?iaeaio aeeiai?/iiai aaeainoaaiiy oo?a?i, ui oaeaeei
iaa?oathoueny, noai?aiiy iiooaeieo oeaio?eooa i o.ae. ?i?oe?aoi?ii
?icaeoeo oai?aoe/ieo i aenia?eiaioaeueieo iaoiae?a aeine?aeaeaiiy NCOO o
aeaeyae? oaa?aeiai o?ea ia no?oi? aoa aeaaeai?e I.TH. Ioeiinueeee, i?ae
ea??aieoeoaii yeiai io?eiaii iaeaaaeeea?o? ?acoeueoaoe a oe?e iaeano?.
Aaeeeee aianie a ?ica’ycaiiy caaea/? no?eeino? noaoe?iia?ieo ?oo?a o?ea
ia no?oiiiio i?aea?n? aoei aianaii N.A. Iaeaoaieii, A.I.?oaaiianueeei,
A.A. ?oi’yioeaaei, A.I. Noi?iaeaieii, I.?. Oai/aiei oa ?i.

Ua a 60-i ?iee c’yaeeenue eiino?oeoe?? eini?/ii? oaoi?ee, ui
i?aaenoaaeythoue niaith noeoii?noue NCOO. Cie?aia, oea iia’ycaii c
i?iaeaiith ?ic?iaee nenoai i???ioaoe?? i noaa?e?caoe?? ?ooo ia’?eo?a, ui
?ooathoueny a oeaio?aeueiiio iuethoiiianueeiio iie? nee. Aea/aiith
no?eeino? noaoe?iia?ieo ?aaeei?a NCOO, ui ?ooathoueny ii i?a?o?,
i?enay/ai? i?aoe? E.I. Ao?eaeiai(, E. Aiooaiao?aa, E. E?eiaa, A.A.
Na?e/aaa oa ?i.

A 1972 ?. ia XIII I?aeia?iaeiiio eiia?ani c oai?aoe/ii( i i?eeeaaeii(
iaoai?ee I.TH. Ioeiinueeee iinoaaea caaea/o i?i aecia/aiiy oiia
no?eeino? ??aiii??ieo iaa?oaiue nenoaie aeaio aaaeeeo a??ineii?a
Eaa?aiaea, ca’ycaieo ?aeaaeueiei noa?e/iei oa?i??ii, iaeei c yeeo ia?
ia?ooiio oi/eo. Iiaoaeiaai? I.A. Oa?eaiiaei o 1971 ?ioe( ??aiyiiy ?ooo
nenoaie n ca’ycaieo oaa?aeeo o?e aeyaeeenue aeiyoeiai c?o/ieie aeey
?ica’ycaiiy oe??? oa ?ioeo iiae?aiiai oeio caaea/. Aeei?enoiaoth/e
??aiyiiy, io?eiai? I.A.Oa?eaiiaei, oa ?o ia?o? ?ioaa?aee, I.ss. Naa/aiei
a 1974 ?. anoaiiaea iaiao?aei? i aeinoaoi? oiiae no?eeino? ??aiii??ieo
iaa?oaiue nenoaie aeaio a??ineii?a Eaa?aiaea. I?e aiae?c? iaiao?aeieo
oiia no?eeino? aoa ciaeaeaiee oe?eaaee aoaeo noaa?e?caoe?? a??ineiia
Eaa?aiaea, ui ia?aaoaa? a noai? niieith, ?ioei, ui iaa?oa?oueny. Oeae
aoaeo aoa aeaoaeueii aeine?aeaeaiee I.ss. Naa/aieii oa eiai o/iyie.

Iiaeaeueoee ?icaeoie aeeiai?ee nenoaie o?e, ca’ycaieo ?aeaaeueieie
oa?i??aie, ciaia’ycaiee aaeeeiio eieo i?eeeaaeieo caaea/, oaeeo ye:
??aiii??i? iaa?oaiiy ianeiao?e/ieo o?e, ??aiii??i? iaa?oaiiy nenoaie
ai?inoaoia, ?aaoey?i? i?aoean?? CCOO, NCOO c a?a?oth/ith oi/eith
i?aea?no, noaoe?iia?i? ?ooe NCOO, ui ia iathoue ia?ooiii? oi/ee i o.ae.
?ica’ycaiith oeeo caaea/ i?enay/ai? i?aoe? E.Ae. Aeoeaiea,
I.I. Aie/oea, A.A. Ai??a, Ae.Ae. Eauaiea, I.ss. Naa/aiea,
A.I.  Nainiiiaa, A.I. Noi?iaeaiea, I.?. Oai/aiei, A.I. Ooeuea?ia oa
?i.

?ioaineaiee ?icaeoie ia/enethaaeueii? oaoi?ee, ?icoe?aiiy (?
iiaeeeainoae, ciaeoei ?e canoinoaaiiy i i?e aea/aii? NCOO. Aoee
?ic?iaeai? i?ia?aie, ui aeicaieythoue: neeanoe ooieoe?th Eaa?aiaea;
eiiaa?ecoaaoe ??aiyiiy ?ooo; aeine?aeeoe no?ee?noue noaoe?iia?ieo
?aaeei?a; i?iaanoe aneiioioe/ia ?ioaa?oaaiiy ??aiyiue. C oeeie caaea/aie
iia’ycai? ?iaia E.A. Ao?eaeiai?, A.Ae. I?oaaiaa, Ae.I. Eeiiiaa,
A.I. Ia?ea?aa, A.A. Nieieueneiai, I.A. Ii/oa?aiea oa ?i.

Ooieoe?iioaaiiy no/anieo eini?/ieo aia?ao?a i aeine?aeaeoaaieo ?aeao a
?aaeueieo oiiaao iieacaei, ui ia’?eoe oaeiai ?iaeo ? cia/ii iaioa
aei?noeeie, i?ae oea aeieeaaei c ia?aaeiieueioieo aei?iaoaaiue. Oea
aeiaaaei aaaaeaiiy i?oaeiino? a i?iiiiiaaio iiaeaeue. W.D. Sundberg
i G.F. Reis cai?ieee i?oaeiee ei?ion ?aeaoe nenoaiith aeaio o?e,
ca’ycaieo i?oaeiei oa?i??ii. Iaa?oue oaea iaaeeaeaia iiaeaeue aeaea
?acoeueoaoe, ui aeineoue aeia?a ca?aaeenue c aeaieie aenia?eiaioo.

I?e aea/aii? aeeiai?ee i?oaeieo ia’?eo?a aaeeeo ?ieue a?ae?a?a? aea??
oaeeo iiaeaeae, ye? aeinoaoiuei iiaii a?aeia?aaeaee a iniiai?
aeanoeaino? ia’?eoo i, a oie aea /an, aeinoaoiuei eaaei i?aeaeaaaeenue
aiae?co. V.E. Cochcran i D.E. Christensen ?icaeyioee aea? iiaeae?
?aeaoe: i?oaeiee noa?aeaiue i nenoaio aeaio o?e, ca’ycaieo i?oaeiei
oa?i??ii. Io?eiai? ?acoeueoaoe /enaeueiiai ?ioaa?oaaiiy aoee ii??aiyi? c
aeaieie aenia?eiaioo. Aeyaeeinue, ui iaeaea? iiaeae? aeaee aeia?ee ca?a
c aenia?eiaioii ii ia?aiao?ao, ui oe?eaaeee aaoi??a.

I?eaaaeaiee ei?ioeee iaeyae na?ae/eoue i?i ??ciiiai?oi? canoinoaaiiy
NCOO i?e iiaeaethaaii? ??cieo oaoi?/ieo ia’?eo?a i aaeeeo e?euee?noue
i?aoeue ii aeine?aeaeaiith ?ooo NCOO (c ne?i/aiiei /eneii o?e a nenoai?.

Aenia?eiaioaeueia i?aeoaa?aeaeaiiy oni?oiiai aeei?enoaiiy NCOO i?e
iiaeaethaaii? i?oaeieo eiino?oeoe?e c?iaeei aeooaeueiith caaea/o
aea/aiiy ?ooo NCOO, /enei o?e a ye?e iaiaiaaeaii c?inoa?, i aeiaaaeaiiy
i?e oeueiio i?aaii??iino? cai?ie iaia?a?aii? iiaeae? neii/aiiiii?iith.

Ne?ae a?aei?oeoe, ui i?e ?ica’ycaii? eiie?aoieo caaea/, a yeeo
aeei?enoiao?oueny noa?aeiaaa iiaeaeue, io?eio?oueny ye nenoaia cae/aeieo
aeeoa?aioe?aeueieo ??aiyiue, oae i nenoaia ??aiyiue c /anoeiieie
iio?aeieie, ui iienothoue iae? i?oaei? eieeaaiiy. I?e oeueiio aeey
?ica’ycaiiy inoaii?o aeei?enoiao?oueny neii/aiiiii?ia aeene?aoecaoe?y,
yea i?eaiaeeoue oe? ??aiyiiy aei nenoaie cae/aeieo aeeoa?aioe?aeueieo
??aiyiue. O aeiaaeeo, eiee i?e ?ica’ycaii? caaea/? aeei?enoiao?oueny
neii/aiiiii?ia iiaeaeue o aeaeyae? nenoaie ca’ycaieo oaa?aeeo o?e, ie
ia?ii aeene?aoecaoe?th aaea ia ??ai? iiaeaethaaiiy nenoaie i
eiino?oeoeai? iaoiaee aiae?oe/ii? iaoai?ee i oai??? cae/aeieo
aeeoa?aioe?aeueieo ??aiyiue aeey aeine?aeaeaiiy io?eiaii? iiaeae?.
Ia?aaaaith ae?oaiai i?aeoiaeo, oaeei /eiii, ? c iaeiiai aieo aoaeoeaiee
oi?iae?ci caieno ??aiyiue ?ooo NCOO (iiaeeeai i c aeei?enoaiiyi AII),
?icaeiooee iaoaiaoe/iee aia?ao aea/aiiy neii/aiiiii?ii? iiaeae?, ui
aeicaiey? a ?yae? caaea/ io?eiaoe aeinooii? aeey iaeyaeo aiae?oe/i?
ioe?iee, a c ae?oaiai aieo — iayai?noue aeine?aeaeaiue, ui
i?aeoaa?aeaeothoue aeia?ee ca?a io?eiaieo ?acoeueoao?a c aeaieie
aenia?eiaioo.

Iaei??th c ia?oi/a?aiaeo caaea/ aea/aiiy neii/aiiiii?ieo nenoai ?
aeine?aeaeaiiy no?eeino? ?o noaoe?iia?ieo ?aaeei?a. Oey caaea/a aaaeeeaa
o ca’yceo c oei, ui ye?ac oe? ?ooe a?aeiia?aeathoue iniiaiei ?iai/ei
?aaeeiai i?oaeieo eiino?oeoe?e, a ?o no?ee?noue aa?aioo? iaae?eia
ooieoe?iioaaiiy oaoi?/ieo ia’?eo?a.

Oaeei /eiii, iaiao?aei?noue ?ic?iaee oai??? aeine?aeaeaiiy NCOO o
canoinoaaii? aei aea/aiiy aeeiai?ee i?oaeieo ia’?eo?a caeeoa?oueny
aeooaeueiith i aei oeueiai /ano, i naia oe?e i?iaeai? i?enay/aia
aeena?oaoe?eia ?iaioa.

Ca’ycie ?iaioe c iaoeiaeie i?ia?aiaie, ieaiaie, oaiaie. Aeine?aeaeaiiy
ii aeena?oaoe?ei?e ?iaio? i?iaiaeeeenue o a?aeiia?aeiino? c Ieaiaie
iaoeiaeo aeine?aeaeaiue a?aeae?e?a oaoi(/ii( iaoai?ee i i?eeeaaeii?
iaoai?ee IIII IAI Oe?a?ie ca?aeii iinoaiiae I?aceae?? IAI Oe?a?ie ii
ianooiieo athaeaeaoieo oaiao:

1986 — 1990 ?iee — “?ic?iaea i ?icaeoie iaoaiaoe/ieo iaoiae?a
?ica’ycaiiy caaea/ aiae?oe/ii? aeeiai?ee, i???ioiaaieo ia canoinoaaiiy a
no/ani?e oaoi?oe?”,

1990 — 1995 ?iee — «?ic?iaea iaoaiaoe/ieo iiaeaeae neeaaeieo iaoai?/ieo
nenoai i iaoiae?a ?o aeine?aeaeaiiy ?c canoinoaaiiyi aei caaea/
iaoeiiaoaeoaaiiy»;

1996 — 2000 ?iee — «Iaoaiaoe/i? iaoiaee eiino?oeoeaiiai aeine?aeaeaiiy
no/anieo i?iaeai no?eeino?, ea?oaaiiy i aeeiai?ee aca?iiae?th/eo o?e»,

a oaeiae o 1997 — 1998 ?ieao a ?aieao i?iaeoo 1.4/155 “Iaoaiaoe/i?
iaoiaee eiino?oeoeaiiai aeine?aeaeaiiy no/anieo i?iaeai aeeiai?ee NCOO”
Aea?aeoiiaeo ooiaeaiaioaeueieo aeine?aeaeaiue I?i?noa?noaa Oe?a?ie a
ni?aaao iaoee i oaoiieia?e.

Iaoa i caaea/? aeine?aeaeaiiy. Iaoith aeaii? aeena?oaoe?eii? ?iaioe ?:

?ic?iaea iaoaiaoe/ii? iiaeae? ?ooo i?oaeiiai ia’?eoo ia iniia? NCOO i
anoaiiaeaiiy aaeaeaaoiino? aeene?aoii? i iaia?a?aii? iiaeaeae.

Aeiaaaeaiiy no?eeino? io?eiaieo neii/aiiiii?ieo ??cieoeaaeo ??aiyiue.

Iiaoaeiaa caaaeueii? oai??? aeey ciaoiaeaeaiiy ?aciiainieo /anoio, a
ieie? yeeo aeieea? iano?ee?noue noaoe?iia?ieo ?oo?a NCOO i?e iiya?
aeenaaeaino a nenoai?.

?ic?iaea eiino?oeoeaiiai aeai?eoio aeine?aeaeaiiy ?ooo NCOO a ieie?
?aciiainieo /anoio.

Iaoeiaa iiaecia io?eiaieo ?acoeueoao?a. A aeai?e ?iaio? aia?oa io?eiaii
iae?i?ei? ??aiyiiy /ioe?ueio iniiaieo iaoai?/ieo iiaeaeae: NCOO, ui
ooai?ththoue iaiiacaieiaiee eaioetha; cae??ieai? NCOO, iaa?euei? oa
a?euei? NCOO.

Anoaiiaeaii, ui an? oe? ??aiyiiy i?eioneathoue ?ica’ycie, yeee iieno?
??aiii??i? iaa?oaiiy ia’?eoo ye oe?eiai iaaeiei caaaeueii? in?.

Ciaeaeaii eiao?oe??io aei?noeino? i?oaeiiai oa?i??o, i?e yeiio ??aiyiiy
?ooo NCOO, eiiaa?eciaaii a ieie? oeueiai ?ica’yceo, i?e ca?eueoaii?
/enea o?e a nenoai? iaaeeaeathoueny aei ??aiyiue iaeeo eieeaaiue
noa?aeiy c a?aeiia?aeieie a?aie/ieie oiiaaie.

?ic?iaeaii aeai?eoi aeiaaaeaiiy ca?aeiino? ?ica’yce?a io?eiaieo ??aiyiue
neii/aiiiii?ieo nenoai aei ??aiyiue a?aeiia?aeieo iaia?a?aieo
aeeoa?aioe?aeueieo nenoai.

Ciaeaeaii oiiae ?nioaaiiy i?aoean?eieo ?oo?a o NCOO, ui ooai?th?
iaiiacaieiaiee eaioetha.

Aeaii iiaeaeueoee ?icaeoie aeine?aeaeaiiy no?eeino? ??aiii??ieo
iaa?oaiue a?eueii? i iaa(eueii( NCOO iaaeiei iaaeaoi?iiaaii? in?
neiao??? i?e a?aooaaii? ciai?oi?o nee i iiiaio?a.

Io?eiaea ?icaeoie oai??y ?aciiainieo /anoio. Aia?oa cai?iiiiiaaii
eiino?oeoeaiee aeai?eoi aecia/aiiy «?aciiainieo» /anoio, a ieie? yeeo
?oo NCOO c iaeith ianeiao?i?th iano?eeee. Cai?iiiiiaaii iaoiae
ciaoiaeaeaiiy ?aciiainieo /anoio i?e aea/aii? ??aiyiue ?ooo neiao?e/ieo
NCOO i eieaeueiiai aeine?aeaeaiiy ??aiyiue ?ooo ianeiao?e/ieo NCOO a
ieie? oeeo /anoio. Aeae?eaii aeaa oeie ?aciiainieo /anoio i ?ic?iaeaii
iaoiae ?o aecia/aiiy. I?aoeacaeaoi?noue i aoaeoeai?noue oeeo aeai?eoi?a
ia?aa??ai? ia i?eeeaaeao ??cieo iaoai?/ieo ia’?eo?a. I?iaaaeaii
ii??aiyiiy ?aciiainieo /anoio i?e ca?eueoaii? e?eueeino? o?e o NCOO i
anoaiiaeaii ?o ca?aei?noue aei a?aeiia?aeieo /anoio noa?aeiaai? nenoaie.

I?aeoe/ia cia/aiiy ?acoeueoao?a aeine?aeaeaiiy. Aeai? ?acoeueoaoe
iathoue ianooiia i?aeoe/ia cia/aiiy:

1. Ine?eueee an? ?aaeueii ?nioth/? ia’?eoe iathoue ianeiao?ith, ciaiiy
?aciiainieo /anoio iaiao?aeii i?e aeai?? ?iai/eo ?aaeei?a eiino?oeoe?e;

2. Aeiaaaeaia ca?aei?noue neii/aiiiii?ii? iiaeae? aei iaia?a?aii?
aeicaiey? ii aenia?eiaioaeueieo aeaieo aecia/eoe eiie?aoia /enei o?e a
NCOO aeey aaeaeaaoiiai iiaeaethaaiiy, a oea aea? iiaeeea?noue aoaeoeaii
?ica’ycoaaoe iinoaaeaio caaea/o;

3. Ciaiiy oiia no?eeino? ?iai/eo ?aaeei?a aeicaiey? ?aoe?iiaeueii
aeae?aoe ia?aiao?e eiino?oeiaaiiai ae?iao.

Ioae?eaoe?? i iniaenoee aianie caeiaoaa/a a ni?eueieo ioae?eaoe?yo.
?acoeueoaoe aeena?oaoe?eii? ?iaioe iioae?eiaai? a iiiia?ao?? [1],
noaooyo [2-19], i?aoeyo eiioa?aioe?e [20, 21].

A iiiia?ao?? [1] caeiaoaa/o iaeaaeaoue ?acoeueoaoe ioieo?a 1.3 — 1.8;
3.5 — 3.9 i /aoaa?oa aeaaa.

A ?iaio? [2] — ?acoeueoaoe ae?oaiai ioieoo.

A ?iaio? [3] caeiaoaa/ai io?eiaii ??aiyiiy ?ooo nenoaie o?e a
na?aaeiaeu?, ui /eieoue ii??, ciaeaeaii ?aciiaini? /anoioe i anoaiiaeaii
iano?ee?noue noaoe?iia?ieo ?ica’yce?a a ?o ieie?.

A noaoo? [4] — io?eiaii ??aiyiiy ?ooo NCOO i anoaiiaeaii aieea i?oaeiiai
ca’yceo ia no?ee?noue ??aiii??ieo iaa?oaiue.

A ?iaio? [5] caeiaoaa/ai i?iaaaeaii aeine?aeaeaiiy aieeao aeiaeaoeiaeo
noaiai?a a?eueiino?, aeeeeeaieo iayai?noth oa?i??a ia no?ee?noue
noaoe?iia?ieo ?oo?a.

A noaoo? [7] caeiaoaa/o iaeaaeeoue i?aea?? i ioe?iea e?oa?aoo?e ii
no?eeino? noaoe?iia?ieo ?oo?a.

A noaoo? [9] — iinoaiiaea caaea/? i oai?aoe/ia /anoeia.

A ?iaio? [10] caeiaoaa/ai caienaii ??aiyiiy ?ooo nenoaie, ui ooai?th?
iaiiacaieiaiee eaioetha, i anoaiiaeaii oiiae ?nioaaiiy o ia?
i?aoean?eieo ?oo?a.

A ?iaioao [18], [20] caeiaoaa/ai iinoaaeaia caaea/a i caienai? ??aiyiiy
?ooo nenoaie, ui aea/a?oueny.

Ai?iaaoe?y ?acoeueoao?a. ?acoeueoaoe aeine?aeaeaiiy aeiiia?aeaeenue :

ia *aoaa?o?e ?anioae?eainuee?e ia?aae? c i?iaeai aeeiai?ee oaa?aeiai
o?ea (i.Aeiiaoeuee, 1984),

V-oiio Ananithciiio c’?cae? c iaoai?ee (i.Oaoeaio, 1995),

V-ie Ananithci?e *aoa?anueeie eiioa?aioe?? “Aiae?oe/ia iaoai?ea,
no?ee?noue i ea?oaaiiy ?ooii” (i.Eacaiue, 1987),

?icoe?aiiio can?aeaii? nai?ia?o ?inoeoooo i?eeeaaeii? iaoaiaoeee ?i.
I.I. Aaeoa (i.Oaieini,1989),

?anioae?eainuee?e eiioa?aioe?? “Aeeiai?ea oaa?aeiai o?ea i no?ee?noue
?ooo” (i.Aeiiaoeuee, 1990),

XV — XVII iaoeiaeo /eoaiiyo ii einiiiaaoeoe? (i.Iineaa, 1991 — 1993),

Second international conference on difference equations and applications
(Hungary, 1995),

I?aeia?iaeiiio iaoeiai-iaoiaee/iiio nai?ia?? “Iaoaiaoe/i? iiaeae?
o?ce/ieo i?ioean?a i ?o aeanoeaino?” (i.Oaaai?ia, 1996),

International conference stability, control and rigid bodies dynamic
(Donetsk, 1996),

I?aeia?iaei?e eiioa?aioe?? “Iaoaiaoeea a (iaeono?i?” (i.Oaaai?ia, 1998),

VI International conference on differential equations and applications
(Poland,1998),

nai?ia?ao a?aeae?e?a i?eeeaaeii? iaoai?ee i oaoi?/ii? iaoai?ee IIII IAI
Oe?a?ie i?ae ea??aieoeoaii I.A. Oa?eaiiaa, I.ss. Naa/aiea,

nai(ia?( a(aeae(e(a aiae(oe/ii( iaoai(ee ( aeeiai(ee aaaaoiaei(?ieo
nenoai (inoeoooo iaoaiaoeee (i.Ee(a) i(ae ea?(aieoeoaii A.I. Eioeyeiaa,
(.I. Eoeianueeiai,

nai(ia?( eaoaae?e oai?aoe/ii( iaoai(ee Ee(anueeiai (inoeoooo
cae(cie/iiai o?ainii?oo i(ae ea?(aieoeoaii E.A. Eiaana.

No?oeoo?a ?iaioe. Aeena?oaoe?eia ?iaioa neeaaea?oueny c anooio, naie
?icae?e?a, aeniiae?a, nieneo aeei?enoaii? e?oa?aoo?e c 171 iaeiaioaaiiy,
iaethie?a ia 10 a?eooao. Caaaeueiee ia’?i ?iaioe 269 noi??iie.

EI?IOEEE CI?NO ?IAIOE

O anooi? iaa?oioiaaii iaiao?aei?noue i?iaaaeaiiy aeine?aeaeaiiy i
aeooaeuei?noue oaie; noi?ioeueiaaii iaoo ?iaioe; a?aei?/aii iiaecio
io?eiaieo ?acoeueoao?a, ?oi? oai?aoe/ia i i?eeeaaeia cia/aiiy.

A ia?oiio ?icae?e? aeaii iaeyae e?oa?aoo?e ii oai? aeena?oaoe??.
A?aei?/aii iniiai? iai?yiee aeine?aeaeaiue neii/aiiiii?ieo NCOO.
Cae?i/o? ?icae?e ei?ioea ?acthia, ui noino?oueny iaiao?aeiino?
i?iaaaeaieo aeine?aeaeaiue i ?o iiaeaeueoi? ?ic?iaee.

Ae?oaee ?icae?e i?enay/aiee aeeeaaeo caaaeueii? iaoiaeeee i
iniiaieo iaoiae?a aeine?aeaeaiiy, ui canoiniaothoueny a aeai?e ?iaio?.
I?eaaaeaii iaiao?aei? oai?aie aiae?oe/ii? aeeiai?ee, oai??? iao?eoeue,
oai??? ??cieoeaaeo noai i oai??? no?eeino? ca Eyioiiaei.

O?ao?e ?icae?e aeena?oaoe?? i?enay/aiee neeaaeaiith ??aiyiue ?ooo NCOO
aeey iiaeaethaaiiy noa?aeiaaeo eiino?oeoe?e c ??cieie oiiaaie ia
e?ioeyo:

Noa?aeaiue (c caaeaiei ?ooii o ia?ooiiiio i?inoi?? (cie?aia, c aeaiia

iii?aie ia e?ioeyo).

2. I?oaeia eiinieue.

3. Noa?aeaiue c iaeiei a?eueiei i iaeiei i?oaeii iaia?oei
e?ioeai.

4. Noa?aeaiue c aeaiia a?eueieie e?ioeyie.

Oeei a?aie/iei caaea/ai o neii/aiiiii?iiio aeiaaeeo a?aeiia?aeathoue:

Nenoaie c iaiiacaieiaiei eaioethaii (?oo aeaio oi/ie e?ioeaaeo o?e

i?aeei?y?oueny caaeaiei ca’yceai);

2. Cae??ieai? nenoaie (ia?oa o?ei ia? aea? ia?ooii? oi/ee);

3. Iaa?euei? nenoaie (ia?oa o?ei ia? iaeio ia?ooiio oi/eo);

A?euei? nenoaie (iaia? ia?ooiieo oi/ie).

). O aaeoi?i?e oi?i? aiie iiaeooue aooe caienai? oae:

= Fk + Rk — Rk+1 (1)

aea

iana o?ea Sk,

oaeaee?noue oi/ee Ck, ui ? oeaio?ii ian o?ea Sk,

Fk — aaeoi? ciai?oi?o nee,

Ak — oaici? ?ia?oe?? o?ea Sk a oi/oe? Ok,

( aaniethoia eooiaa oaeaee?noue o?ea Sk,

oaeaee?noue oi/ee Ok,

Nk — iiiaio ciai?oi?o nee,

ck=OkCk , hk=OkOk+1

I?eioneaeinue, ui c aieo o?ea Sk — 1 ia o?ei Sk ae?? neea
?aaeoe?? Rk , iiiaio neee ?aaeoe?? Lk i i?oaeiee iiiaio Mk, a c aieo
o?ea Sk+1 — neea ?aaeoe?? — Rk+1 , iiiaio neee ?aaeoe?? — Lk+1 i
i?oaeiee iiiaio — Mk+1.

), ui aoiaeeoue a NCOO, caieno?oueny ye ??aiyiiy ?ooo iaeiiai
oaa?aeiai o?ea, aei yeiai aeiaeaoeiai i?eeeaaeai? neee i iiiaioe nee
?aaeoe?e, ui cai?iththoue ae?th non?aei?o o?e. I?e oeueiio a ??aiyiiyo
(1), (2) iio??aii iieeanoe:

A NCOO c iaiiacaieiaiei eaioethaii

,L1=Ln+1=M1=Mn+1=0.

A cae??ieaieo NCOO

,L1=Ln+1=M1=Mn+1=Rn+1=0.

Aeey iaa?eueieo NCOO

=0, L1=Ln+1=Mn+1=Rn+1=0.

Aeey a?eueieo NCOO

L1=Ln+1=M1=Mn+1=R1=Rn+1=0.

Iieeaaeaeinue, ui o?ea, c’?aeiai? i?ae niaith oa?i??aie, ye?
i?eioneathoue o a?aeiiniiio ?on? eeoa /enoa iaa?oaiiy. Aei oaeeo oei?a
oa?i???a iaeaaeaoue oeee?iae?e/iee, oi?aa?naeueiee i noa?e/iee oa?i??e,
ui i?eioneathoue o a?aeiiniiio ?on? a?aeiia?aeii iaeei, aeaa i o?e
noaiaiy a?eueiino?.

Iaeiae, ye iieacaii a ioieo? 3.6, iiaeia aaaaeaoe, ui an? o?ea c’?aeiai?
noa?e/ieie oa?i??aie, aea o aeiaaeeo iayaiino? oi?aa?naeueiiai aai
oeee?iae?e/iiai oa?i??a, aei ieo i?eeeaaeai? aeiaeaoeia? neee i iiiaioe
nee ?aaeoe?e ca’yceo, a aaaaeai? iaaei??i? ci?ii? i?aeei?ythoueny
aeayeei aieiiiiiei ca’yceai.

noai o(ea a ?ia?oe?eiiio i?inoi??, oi i?e oiia?, ui o?ea Sk i Sk+1
ca’ycai? oeee?iae?e/iei oa?i??ii, oe? ci?ii? iiaeii? caaeiaieueiyoe
ianooiiei ??aiyiiyi ca’yceo:

(3)

(4)

iiaeii? caaeiaieueiyoe ni?aa?aeiioaiith (3).

Aeae? iieacaii, ye, aeei?enoiaoth/e ??aiyiiy ca’yceo i a?aeii? ??aiyiiy
?ooo NCOO (c noa?e/ieie oa?i??aie, caienothoueny ??aiyiiy ?ooo NCOO c
oi?aa?naeueieie i oeee?iae?e/ieie oa?i??aie. Oaeee i?aeo?ae a
a?eueoino? caaea/ aea? iaea?eueo aeinooiio aeey iaeyaeo oi?io ??aiyiue
?ooo ia?oiai iaaeeaeaiiy.

Iio??aii a?aei?oeoe, ui yeui aeey NCOO c iaiiacaieiaiei eaaoethaii i
cae??ieaii? NCOO ?niothoue ?ooe, iia’ycai? eeoa c i?oaeieie eieeaaiiyie,
oi iaa?eueia i a?eueia NCOO, e??i i?oaeieo eieeaaiue, ?ooathoueny ye
iaeia oe?ea a ?ia?oe?eiiio i?inoi??. Aeey oeeo nenoai aeae?eaii ?oo
ia’?eoo a oe?eiio i iae? i?oaei? eieeaaiiy, ye? a?aeiia?aeii iacaai?
aaeeeei i iaeei ?ooaie. I?eioneaeinue, ui a?aeiini? i?oaei? i?iaeie iae?
i ??aiyiiy ?ooo e?i?ei? ii /anoei? ci?iieo. Oae? ??aiyiiy aeey noa?aeiy
c iaeiei iaia?oei i iaeiei a?eueiei e?ioeyie oa iaa?eueii( i a?eueii(
NCOO io?eiaii a ioieoao 3.7 — 3.9.

*aoaa?oee ?icae?e i?enay/aiee a?aie/iiio ia?aoiaeo a ??aiyiiyo ?ooo
aaaaeaiieo NCOO ? anoaiiaeaiith a?aeiia?aeiino? ??ceeo ne?i/aiiii??ieo ?
iaia?a?aieo caaea/.

(l — aeiaaeeia noa?aeiy). Iiia? k-ai oa?i??a, aiaeia?/ii A.Aienoaeio,
o?aeooaaany, ye eii?aeeiaoa ii in? OZ (OZ — a?nue neiao??? noa?aeiy),
zk=kh oiae? xk=xk(zk), yk=yk(zk).

Aoei anoaiiaeaii, ui yeui aei?noe?noue noa?aeiy EJ i aei?noe?noue
oa?i??a e2 caaeiaieueiythoue ni?aa?aeiioaiith

(5)

oi aaee/eia i?oaeiiai iiiaioo a oa?i??? i?yio? aei iiiaioo, ae?th/iai a
ieineiio ia?aoei? noa?aeiy.

i?yiothoue aei ??aiyiue aaeeeiai ?ooo i?oaeiiai noa?aeiy.

C a?aeiieo ni?aa?aeiioaiue, ui ae?aaeathoue iio?aei? /a?ac ne?i/aii?
??cieoe?, i a?aie/ieo cia/aiue aeey eiao?oe??io?a ??aiyiue iaeiai ?ooo
NCOO aoei aeiaaaeaii, ui i?e aeai?? aei?noeino? oa?i??a ca?aeii (5),
??aiyiiy iaeiai ?ooo NCOO i?yiothoue aei ??aiyiue iaeiai ?ooo i?oaeiiai
noa?aeiy.

c a?aeiia?aeieie ??aiyiiyie iaeeo eieeaaiue i?oaeieo noa?aei?a.

Ioieo 4.3 i?enay/aiee aea/aiith ?ooo NCOO i aaeee Oeiioaiea a
iaei?ino?oiio aeiaaeeo.

(6)

??aiyiue ?ooo NCOO c ??aiyiiyie iaeeo eieeaaiue i?oaeieo noa?aei?a.

I’yoee ?icae?e i?enay/aiee aeiaaaeaiith ca?aeiino? ?ica’yce?a ??aiyiue
?ooo NCOO aei ?ica’yceo ??aiyiue iaeeo eieeaaiue noa?aeiaaeo iiaeaeae.

A ioieo? 5.1 i?iaaaeaii aiae?c aeanieo /anoio eieeaaiue a?eueii? NCOO,
ui ?ooa?oueny ca ?ia?oe??th. I?eioneaeinue, ui NCOO neeaaea?oueny c n
iaeiaeiaeo a??ineii?a Eaa?aiaea i iiaeaeth? i?oaeiee noa?aeiaaee ia’?eo
aeiaaeeiith l , oeaio?aeueieie aeaaoi??aeueieie iiiaioaie ?ia?oe?? A i B
i ianith M. Oiae? aeey NCOO ia?ii

(7)

aeae?aee ca?aeii (5).

ciaeaeaii aeaaa?a?/ia ??aiyiiy

(8)

eiao?oe??ioe yeiai caeaaeaoue a?ae aaiiao?e/ieo i ianiaeo ia?aiao??a,
cacia/aieo a (7).

(n1+n2=n).

Caaaeyee i?iaaaeaiei ia?aoai?aiiyi, aeani? /anoioe aeey n=2,3 iiaeooue
aooe aecia/ai? a yaiiio aeaeyae?.

Aeani? /anoioe noa?aeiaai? iiaeae? aecia/aeenue ye ei?ai?
o?ainoeaiaeaioiiai ??aiyiiy

(9)

io?eiaiiai I.I. ?etho?iei.

*enaeueiee ?ica’ycie (8), (9) aeicaieea anoaiiaeoe ca?aei?noue /anoio
neii/aiiiii?ii? iiaeae? aei /anoio noa?aeiaai?, ui caeaee ?ac na?ae/eoue
i?i i?eeiyoi?noue cai?iiiiiaaii? aeene?aoii? iaoaiaoe/ii? iiaeae?.

iaaeiei nai?? iaaeaoi?iiaaii? in? neiao???, i i?e oeueiio eiai
aeaiaioe cae?eniththoue iinooiaeuei? i iaa?oaeuei? ?ooe iaaeiei aieiaieo
inae ?ia?oe?? ia?iaiaeeeoey?iiai ia?aoeio, aea i?iaeie, ye( aeeeeeai?
cnoaii, ia a?aoiaothoueny. Neii/aiiiii?iei aiaeiaii oaei? nenoaie ?
nenoaia iaeiaeiaeo a??ineii?a Eaa?aiaea, ca’ycaieo i?oaeiei oa?i??ii ?c
noaeith aei?noe?noth, ui ooai?th? iaiiacaieiaiee eaioetha. Iniaeea?noth
?icaeyiooi( caaea/? ? iayai?noue ?ica’yceo a yaiiio aeaeyae? ye a
iaia?a?ai?e, oae i a neii/aiiiii?iie iiaeae?. Aiie a(aeiia(aeii iathoue
aeaeyae:

(10)

aea

;

(11)

ooo

Oiae? ?c (10), (11) aeieeaa(

Ine?eueee io?eiai? ??aiyiiy ?ooo neii/aiiiii?ii? NCOO iiaeooue
o?aeooaaoeny ye neii/aiii?icieoeaaa noaia ii i?inoi?ia?e ci?ii?e
??aiyiue c /anoeiieie iio?aeieie noa?aeiaai? iiaeae?, a ca?eueoaiiy
/enea o?e a nenoai? ye ca?eueoaiiy e?eueeino? aoce?a n?oee, oi aeoiaey/e
c icia/aiiy oai??? ??cieoeaaeo noai, io?eiaiee ?acoeueoao na?ae/eoue i?i
ca?aei?noue ?ica’yceo aeene?aoii? caaea/? aei aeeoa?aioe?aeueii?.

Ioieo 5.3 i?enay/aiee aea/aiith ?ica’yce?a ??aiyiue iaeeo eieeaaiue
a?aeiinii noaio ??aiiaaae iaeii??aeii? iaaaaiii? eiinie? i ??
neii/aiiiii?iiai aiaeiao — cae??ieaii? NCOO. O oe?e caaea/? ?ica’ycie
aaea ia iiaea aooe aeienaiee a yaiiio aeaeyae? i aeey aeiaaaeaiiy
ca?aeiino? ?ica’yce?a ??cieoeaaeo ??aiyiue aei aeeoa?aioe?aeueieo aoea
aeei?enoaia ianooiia oai?aia oai??? ??cieoeaaeo noai (oai?aia Eaena).

Oai?aia 1. Iaoae ??cieoeaaa noaia Lh uh = fh ai?ieneio? caaea/o Lu=f
ia ?ica(yceo u c ii?yaeeii hk. Oiae? ?ica’ycie uh ??cieoeaai? caaea/?
ca?aa?oueny aei ?ica’yceo [u]h aeeoa?aioe?aeueii?, i?e/iio ia( i(noea
ioe(iea

Aeei?enoaiiy oe??? oai?aie aeicaieeei ?icaeoe aeiaaaeaiiy ca?aeiino? ia
aeaa aoaie:

1. Anoaiiaeaiiy ai?ieneiaoe?? aeeoa?aioe?aeueieo ??aiyiue ??cieoeaaeie.

Aeiaaaeaiiy no?eeino? ??cieoeaai? noaie.

Aoei anoaiiaeaii, ui ai?ieneiaoe?y aeieeaa? ?c a?aie/ieo
ni?aa?aeiioaiue, anoaiiaeaieo i?e aiae?c? ??aiyiiy ?ooo ne?i/aiiii??ieo
nenoai, /enei o?e a yeeo iaiaiaaeaii c?inoa?.

Aeey aeiaaaeaiiy no?eeino? ??cieoeaaeo ??aiyiue iaiao?aeii iieacaoe, ui
iaea cao?aiiy i?aai? /anoeie aeeeeea? ??aiii??ia a?aeiinii h cao?aiiy
?ica’yceo.

??cieoeaaa ??aiyiiy aeey cae??ieaii? NCOO aoei i?eaaaeaii aei aeaeyaeo

(12)

aea

A1=E+G1(n+1)2A0 ; E- iaeeie/ia iao?eoey;

; ann=1;

; bn — 2n — 1=5; b n — 2n — 1=-2; b n — 1n — 1=1;

G1,G2 — aeiaeaoi? eiinoaioe, ui ia caeaaeaoue a?ae h.

Oiae? ??aiyiiy ?c cao?aiith i?aaith /anoeiith oaea

(13)

Aeiaaaeaia aeiaeaoia icia/ai?noue iao?eoe? A1 i a?aooaaiiy neiao??? A1 i
B aeicaieeee caanoe ??aiyiiy (12), (13) aei aeaeyaeo

(14)

aea

— oa?aeoa?enoe/i? /enea iao?eoe? D=A1-1B1 , B1=G2(n+1)4B .

Ii?ia ??cieoe? ?ica’yce?a ??aiyiue (12), (13) c o?aooaaiiyi (14) aoea
ioe?iaia oae :

(15)

eiinoaioaie, ui ia caeaaeaoue a?ae h.

, a

(16)

C ia??aiino? (16) aeieeaa?

(17)

aeani? /enea iao?eoe? D -1 = B1 -1A1 ,

aoea aeei?enoaia a(aeiia a oai?(( iao?eoeue oai?aia.

Oai?aia 2. Aeani? /enea iao?eoe? ia ia?aaeuothoue aoaeue-yei? ?? ii?ie.

Oiae?

(18)

Ca ii?io iao?eoe? aoea aea?aia

(19)

A?aoiaoth/e no?oeoo?o iao?eoe? D -1, ?? aeaiaioe aoee i?aaenoaaeai? oae

(20)

Iao?eoeth B -1 aaeaeiny iiaoaeoaaoe a yaiiio aeaeyae?. ?? eiao?oe??ioe
aei??aiththoue

(21)

I?aenoaiiaea (16) — (21) a (15) aeicaieeea c?iaeoe aeniiaie

aea N — eiinoaioa, yea ia caeaaeeoue a?ae h , ui e aeiaiaeeoue
no?ee?noue ??cieoeaai? caaea/? i ca?aei?noue ?ica’yce?a neii/aiiiii?ieo
??aiyiue aei ?ica’yceo iaia?a?aieo.

A ioieo? 5.4 aea/aany ?ica’ycie ??aiyiue iaeeo eieeaaiue noa?aeiy c
iaeiei iaia?oei i iaeiei a?eueiei e?ioeyie i eiai neii/aiiiii?ii?
iiaeae? iaa?eueii? NCOO. I?e aeiaaaeaii? aeei?enoiaoaaeanue oai?aia 1.
Ine?eueee ai?ieneiaoe?y aaea aeiaaaeaia, oi a oeueiio ioieo?
aeine?aeaeoaaeanue eeoa no?ee?noue ??cieoeaaeo ??aiyiue. Aeey iaa?eueii?
nenoaie ??aiyiiy (12) ia? aeaeyae

(22)

aea

Neiao?e/i?noue iao?eoe? D i aeiaeaoia icia/ai?noue iao?eoe? C
aeicaieeee, aeei?enoiaoth/e cai?io Y=PW1 , aea P=C1-1/2U1 , U1 —
oi?oa?ia iao?eoey, caanoe ??aiyiiy (22) aei aeaeyaeo

, (23)

aea

aeani? /enea iao?eoe? F=C1-1 D, C1 =a2 n4 C.

Aeae?, ye i a iiia?aaeiueiio ioieo?, ii?yae c ??aiyiiyi (23)
aoee caienai? ??aiyiiy ?c cao?aiith i?aaith /anoeiith, i?iaaaeai?
iaiao?aei? ia?aoai?aiiy oeeo ??aiyiue i neeaaeaia ??cieoey (15). ??
ii?ia aeey aeaii? caaea/? ioe?ith?oueny oae

.

Ca?aeii oai?aie 2,

eiinoaioith, ui ia caeaaeeoue a?ae h, ui i ?ica’ycaei iinoaaeaio
caaea/o.

Cai?iiiiiaaiee iaoiae aeiaaaeaiiy ca?aeiino? ?ica’yce?a neii/aiiiii?ieo
caaea/ aei iaia?a?aieo, ye iieacaii a ioieo? 5.4, aeyaeany
eiino?oeoeaiei. A ioieo? 5.5 oeae i?eeii canoiniaaii aei a?eueieo NCOO i
noa?aeiy c aeaiia a?eueieie e?ioeyie. ??aiyiiy neii/aiiiii?ii? iiaeae? a
oeueiio aeiaaeeo ia? aeaeyae (22), aea iao?eoey D oaea

aea eiao?oe??ioe b,d1 ,d2 ia caeaaeaoue a?ae n.

aeani? /enea iao?eoe? D = Gn4B, aea B — neiao?e/ia i’yoeaeiaaiiaeueia
iao?eoey c aeaiaioaie

I?eaaaeaii aeaa iaoiaee ?ica’ycaiiy iinoaaeaii? caaea/?.

Oinoee ?icae?e oe??? ?iaioe i?enay/aii aeaiiino?aoe?? canoinoaaiiy NCOO
aeey aeine?aeaeaiiy aeeiai?ee i?oaeieo ia’?eo?a ia i?eeeaae? oaeeo
caaea/, ye aeae?eaiiy noaoe?iia?ieo ?aaeei?a, ciaoiaeaeaiiy oiia ?o
?nioaaiiy oa aeine?aeaeaiiy no?eeino?.

A ioieo? 6.1 aeae?eaii aeaa iaea?eueo ?iciianthaeaeaieo oeie
noaoe?iia?ieo ?oo?a: ??aiii??i? iaa?oaiiy i ?aaoey?i? i?aoean??.
Anoaiiaeaii, ui ??aiyiiy ?ooo an?o ?icaeyiooeo o ?iaio? NCOO
aeiioneathoue ?ica’ycie, a?aeiia?aeiee ??aiii??iiio iaa?oaiith ia’?eoo,
ye oe?eiai, iaaeiei aa?oeeae?, yea ca?aa?oueny c a?nnth neiao???
ia’?eoo. Aeaii iaeyae ?acoeueoao?a ii aeine?aeaeaiith ?aaoey?ieo
i?aoean?e o iaa?eueii? NCOO. Oiiae ?nioaaiiy ?aaoey?ieo i?aoean?e o
NCOO, ui ooai?th? iaiiacaieiaiee eaioetha, anoaiiaeai? a i?ae?icae?eao
6.1.1 i 6.1.2.

A i?ae?icae?e? 6.1.1 ?icaeyiooi nenoaio n iaeiaeiaeo a??ineii?a
Eaa?aiaea, ca’ycaieo i?oaeieie noa?e/ieie oa?i??aie. Aea/aeanue
iiaeeea?noue ?nioaaiiy o oe??? nenoaie ?aaeeio

(24)

ii a?aeiioaiith aei ia?ooiii?. Oeueiio ?ica’yceo a?aeiia?aea? ?oo
iaoai?/ii? nenoaie, a ye?e eiaeai ?c a??ineii?a cae?enith? ?aaoey?io
i?aoean?th.

sseui i?e oeueiio a?n? neiao??? an?o a??ineii?a eaaeaoue a iaei?e
ieiuei?, oi

(25)

.

I?iaaaeaiee aiae?c aeicaieea anoaiiaeoe, ui ?ica’ycie (24) i?e
oiiaao (25) aeey iaaaaiii? iaoai?/ii? nenoaie ?nio?, yeui

i aeeiio?oueny ni?aa?aeiioaiiy

A i?ae?icae?e? 6.1.2 ?icaeyiooi nenoaio n iaeiaeiaeo aaaeeeo a??ineii?a
Eaa?aiaea, ca’ycaieo oi?aa?naeueieie i?oaeieie oa?i??aie. A oeueiio
aeiaaeeo eooe Aeea?a, ui iienothoue ?ica’ycie (24), iiaeii?
caaeiaieueiyoe ni?aa?aeiioaiith

(26)

Anoaiiaeaii, ui oeae ca’ycie iaeeaaea? iaiaaeaiiy ia eiinoaioe, ui
aecia/athoue ?ica’ycie (24). Iieacaii, ui o aeiaaeeo aeaio o(e i?e
a?aooaaii? (26), ?ica’ycie (24) oaeee:

(27)

i iieno? ?aaoey?io i?aoean?th ae?oaiai o?ea i ??aiii??ia iaa?oaiiy
ia?oiai iaaeiei aa?oeeae?, yea ia ca?aa?oueny c eiai a?nnth neiao???.
Anoaiiaeaii, ui ?ica’ycie (25) ?nio? i?e oiia?

aea

Aeine?aeaeaiiy no?eeino? ??aiii??ieo iaa?oaiue a?eueieo i iaa?eueieo
NCOO i?iaaaeaii a ioieo? 6.2.

A i?aeioieo? 6.2.1 aea/aii ?oo a?eueii? NCOO, ui ciaoiaeeoueny i?ae
ae??th aa?iaeeiai?/ieo nee i iiiaio?a. Anoaiiaeaii ni?aa?aeiioaiiy i?ae
ia?aiao?aie nenoaie, ui oa?aeoa?ecothoue ae?th/a neeiaa iiea, ye?
aeicaieythoue ?e cae?enithaaoe ?oo, a yeiio oeaio? ian nenoaie
?ooa?oueny ??aiii??ii i i?yiie?i?eii i aiia iaa?oa?oueny ye iaeia
oaa?aea o?ei iaaeiei in?, eie?iaa?ii? aaeoi?o oaeaeeino? oeaio?o ian.
Ciaeaeaii iaiao?aei? oiiae no?eeino? oeueiai ?aaeeio i?e oiia?, ui o?ea
? a??ineiiaie Eaa?aiaea, a neeiaa iiea noaoe?iia?ia. I?iaaaeai?
aeine?aeaeaiiy ?ooo NCOO, ui ciaoiaeeoueny i?ae ae??th noia?iiai
aiaeiiaethth/iai iiiaioo, aeicaieeee anoaiiaeoe:

1. ??aiii??i? iaa?oaiiy nenoaie aeaio o?e, ca’ycaieo i?oaeiei oa?i??ii,
aei?noe?noue yeiai aeinoaoiuei aaeeea, no?ee? aneiioioe/ii.

2. Aeey nenoaie neeueii aeoyaiooeo a??ineii?a Eaa?aiaea, ca’ycaieo
i?oaeiei oa?i??ii, ?nio? ?ioa?aae aei?noeinoae oaeeo, ui i?e aeai??
ia?aiao?o aei?noeino? ?c oeueiai ?ioa?aaeo, ??aiii??i? iaa?oaiiy
aneiioioe/ii no?ee? i?e aeinoaoiuei aaeeeeo aei?noeinoyo noathoue
iano?eeeie.

A i?ae?icae?e? 6.2.2 ?icaeyiooi iaa?eueio nenoaio aeaio aaaeeeo
a??ineii?a Eaa?aiaea, ca’ycaieo i?oaeiei oi?aa?naeueiei oa?i??ii.
Aea/aii ??aiii??i? iaa?oaiiy oaei? nenoaie iaaeiei aa?oeeae?. Oey
nenoaia ? i?ii?aeiith i?ae cae??ieaiith i iaa?eueiith NCOO, o yei?
aei?noe?noue noa?e/iiai oa?i??o, ?icoaoiaaiiai a ia?ooii?e oi/oe?,
aei??aith? ioeth. Ciaeaeaii ni?aa?aeiioaiiy i?ae aei?noeinoyie
oi?aa?naeueiiai i noa?e/iiai oa?i???a, i?e yeeo iaiao?aei? oiiae
no?eeino? aeeiiothoueny i?e aeia?euei?e oaeaeeino? iaa?oaiiy NCOO.

Nueiiee ?icae?e aeena?oaoe?eii? ?iaioe i?enay/aiee aeei?enoaiith NCOO
aeey aea/aiiy ia’?eo?a c iaeith ianeiao?i?th.

A ioieo? 7.1 aieea iaei? ianeiao?i? ia no?ee?noue ?ooo i?iaeaiiino?iaaii
ia i?eeeaae? iaeiiai o??aiiaaaeaiiai oaa?aeiai o?ea (oeaio? ian ieae/a
oi/ee iii?e).

?icaeyiooi aeaa aeaee ianeiao?i?:

a eii?aeeiaoe oeaio?o ian — 0,0,c3 .

iae? ia?aiao?e.

Ciaeaeaii /anoioe

(28)

ia? e?aoi? ei?ai?. Anoaiiaeaii, ui iiyaa a nenoai? ianeiao?i?, ye
ia?oiai, oae i ae?oaiai aeaeo, i?eaiaeeoue aei aeieeiaiiy iano?eeino?
noaoe?iia?ieo ?aaeei?a a ieie? /anoioe (28), yeo iaceaa?ii aeae?
?aciiainiith.

aeey nenoai c iaeith ianeiao?i?th. ?icaeyiooi iaoai?/i? nenoaie,
??aiyiiy ?ooo yeeo

(29)

(30)

i?eioneathoue a?aeiia?aeii ?ica’ycee

(31)

(32)

? neaey?. I?eioneaeinue (nioaaiiy iaae?iaeaeaii( cai(ie ci(iieo

,

aea aij — a(aeii( ooieoe(( /ano, ye( i?eaiaeyoue nenoaie (29), (30),
e(iaa?eciaai( a ieie( ?ica’yce(a (31), (32), aei aaoiiiiieo.

Oiae? oa?aeoa?enoe/i? ??aiyiiy nenoai ia?oiai iaaeeaeaiiy caienothoueny
oae:

(33)

(34)

aea

?c ni?aa?aeiioaiue

, i?e yeeo ??aiyiiy (30) ia? e?aoi? ei?ai?. Naia a ieie? oeeo /anoio
o nenoaie (29) iiaeooue aeieeaoe iano?ee? ?ica’ycee (31).

Iiaeaeueoa aeine?aeaeaiiy iia’ycaii c aea/aiiyi ??aiyiiy (29).
Ia/eneth?oueny iio?aeia

i aeae?eythoueny aeaa aeiaaeee:

1. f(a) ia aei??aith? ioeth, oiae?

i i?e aeeiiaii?

?ica’ycie (31) nenoaie (29) aoaea iano?eeee.

f(a)=0, oiae?

i aeine?aeaeaiiy caiaeeoueny aei aiae?co ciaeiaecia/aiinoi eaaae?aoe/ii?
oi?ie

(35)

sseui eaaae?aoe/ia oi?ia (35) aecia/aia aeiaeaoii, oi ?ica’ycie (31)
nenoaie (29) no(eeee, yeui ae aiia ciaeiciiiia, oi a ieie? ?aciiainii?
/anoioe ?nio? ?ioa?aae iano?eeino?.

(36)

??aiyiiy

(37)

ca’ycai? oae:

.

Ca cai?iiiiiaaiith a iiia?aaeiueiio ioieo? iaoiaeeeith ?aciiaini?
/anoioe ?icooeothoueny ye e?aoi? ei?ai? oa?aeoa?enoe/iiai ??aiyiiy
neiao?e/ii? nenoaie.?iaiyiiy (36) ia? e?aoi? ei?ai? a aeaio aeiaaeeao:

;

Oe? /anoioe aoee a?aeiia?aeii iacaai? /anoioaie ia?oiai i ae?oaiai
oei?a.

(38)

aoa i?aaenoaaeaiee o aeaeyae(

,

aea

.

Oiae( a ?(aiyii( (37)

(39)

, a ?aciiainia oaeaee(noue

(40)

iiaeiii caaeiaieueiyoe ni(aa(aeiioaiith

,

( ?aciiainia oaeaee(noue aei?(aith(

(41)

I?e oeueiio oa?aeoa?enoe/ia ?(aiyiiy (36) ia( e?aoiee ei?(iue.

aeey aeoyaiooeo a(?ineii(a. Aea naia oeae aeiaaeie iaea(eueo oe(eaaee,
ine(eueee iaeiei c iaeaaaeeea(oeo canoinoaaiue NCOO ( iiaeaethaaiiy c
(o aeiiiiiaith i?oaeieo noa?aei(a, aeey yeeo, ye a(aeiii, aeiaaeeia
iaaaaaoi ia?aaaaea( (io( e(i(ei( ?ici(?e.

Ii?(aiyiiy iiaeoe(a ?aciiainieo /anoio aeicaieeei anoaiiaeoe

ca(aeee aeieeaa(, ui ae?oa( ?aciiaini( /anoioe aeinyaathoueny i?e
iaioeo oaeaeeinoyo iaa?oaiiy ia((eoo.

, aecia/aieo a (38), (41), i?e iayaiino? ianeiao?i? a NCOO
aeieeathoue ?ioa?aaee iano?eeino?.

A ioieo? 7.4 aei ?ai?oa ?icaeyiooi? NCOO aeiaaaeaii o?ao? o?ei. A
oeueiio aeiaaeeo e?euee?noue ?aciiainieo oaeaeeinoae ca?eueoo?oueny, aea
ia an? aiie iiaeooue aooe aeienai? a yaiiio aeaeyae?. Iaeiae ieae/?,
iniaeeai iaaacia/i? ?aciiaini? oaeaeeino? ye ia?oiai, oae i ae?oaiai
oei?a ciaoiaeyoueny aiae?oe/ii.

Oae, ?aciiaini( oaeaeeino? ia?oiai oeio oae(:

(42)

Ieae/a ?aciiainia /anoioa ae?oaiai oeio aeinyaa(oueny i?e oaeaeeino(
iaa?oaiiy, yea aei?(aith(

(43)

Aiae(c (43) aeicaieea anoaiiaeoe, ui ciaeaeaia /anoioa iaa?oaiiy (nio(
i?e ianooiieo oiiaao, ye( ca’ycothoue ia?aiao?e nenoaie:

,

oiaoi (( (nioaaiiy iiaeeeai ( ia aeey aeoyaiooeo o(e.

Aeae? a oeueiio ioieo? aeey nenoaie n ca’ycaieo oaa?aeeo o?e (n>2)
cai?iiiiiaaii ianooiiee aeai?eoi ciaoiaeaeaiiy ?aciiainieo /anoio aeaio
oei?a.

aea

— neiao?e/i( iao?eoe(, a yeeo

aecia/ai( oi?ioeith (7).

( ?aciiaini( /anoioe ia?oiai oeio ciaoiaeyoueny ye ei?ai( nenoaie

(44)

ui iieaaoo( caaea/o ciaoiaeaeaiiy ei?ai(a.

I?e aecia/aii( cia/aiue ?aciiainieo /anoio ae?oaiai oeio aeae(eythoueny
aeaa aeiaaeee:

(45)

(46)

aea xi — ei?ai( ia?oiai, a yk — ei?ai( ae?oaiai ?(aiyiiy nenoaie (44).

A ia?oiio aeiaaeeo aei ni(aa(aeiioaiue A((oa, caienaieo
a(aeiia(aeii aeey ia?oiai aai ae?oaiai ?(aiyiiy (44), aeiaea(oueny
ca(ycie (45), ?ica(yco(oueny io?eiaia nenoaia ?(aiyiue ( aecia/a(oueny
a?oia ?aciiainieo /anoio.

O ae?oaiio aeiaaeeo aeei?enoiao(oueny cai(ia

i?e?(aith(oueny ioeth ( ia/eneththoueny ?aciiaini( /anoioe.

i?oaeiee ia’?eo iiaeaeth?oueny NCOO, ui neeaaea?oueny c aeaio i o?ueio
o?e. Iieeaaeaeinue, /oi ia’(eo ia( oi?io oeee(iae?a. Oiae( eiai
aeaaoi?(aeueiee e inueiaee iiiaioe (ia?oe(( a(aeiia(aeii aei?(aiththoue

A=M(3R2 +l2 )/12 , B=MR2 /2 ,

aea

R — ?aae(on oeee(iae?a, M — eiai iana, l — aenioa.

Ine(eueee o(ei Sn ( 1/n-oith /anoeiith aeo(aeiiai o(ea, oi

mn =M/n , hn =l/n , Rn =R , cn =l/2n ,

( oiae(

(47)

aea

r=MR2 /12 , s=Ml2 /12.

ca’ycai( ni(aa(aeiioaiiyi

. (48)

I(aenoaiiaea (47), (48) a (38), (42) aeicaiey( i?eaanoe ae?ac aeey
ia?oeo ?aciiainieo oaeaeeinoae aei aeaeyaeo

(49)

, a yeiio i=1,2 iicia/a( oei /anoioe; j = 2,3,…,n — e(euee(noue o(e
o nenoai(, a k = 1,2,3… — e(euee(noue /anoio aeaiiai oeio.

?c (49) aeo(ea(

I?iaaaeai? aiae?oe/i? i /eneia? aeine?aeaeaiiy aeicaieeee anoaiiaeoe, ui
i?e ca?eueoaii? /enea o?e a nenoai? iiaeoe? a?aeiia?aeieo /anoio
ca?eueoothoueny, aea i?e oeueiio ieae/a /anoioa ae?oaiai oeio iaioa
a?aeiia?aeii? /anoioe ia?oiai oeio.

A ioieo? 7.6 aecia/aii ?aciiaini? /anoioe a?eueieo NCOO i i?oaeieo
noa?aei?a c aeaiia a?eueieie e?ioeyie. Anoaiiaeaii ca?aei?noue
?aciiainieo /anoio neii/aiiiii?ii? iiaeae? aei a?aeiia?aeieo /anoio
i?oaeiiai noa?aeiy. Oeae ?acoeueoao ? ua iaeiei i?aeoaa?aeaeaiiyi
iiaeeeaino? aeei?enoaiiy neii/aiiiii?ii? iiaeae? i?e aea/aii? aeeiai?ee
i?oaeieo noa?aeiaaeo nenoai.

A ioieo? 7.7 aeine?aeaeaii aieea iiiaio?a ciai?oi?o nee ia aaee/eio
?aciiainieo /anoio ia?oiai i ae?oaiai oei(a.

Aaaaeaeinue. ui nenoaia ia?aaoaa? i?ae ae??th ciai?oiueiai neeiaiai
iiey. a yeiio aei eiaeiiai o?ea i?eeeaaeaiee iiiaio Ni (i=1,2; M1 =
M2 ). Anoaiiaeaii. ui neeiaa iiea aieeaa? ia aaee/eio ? e?euee?noue
?aciiainieo /anoio.

?aciiaini? oaeaeeino? ia?oiai oeio aei??aiththoue

?aciiaini( ae oaeaeeino( ae?oaiai oeio caaeiaieueiythoue ?(aiyiith

(50)

Ei?ai( ?(aiyiiy (50) iiaeia cia?aceoe o aeaeyae(

iathoue aeaeyae (40), (41).

A caeeth/iiio ioieo? oeueiai ?icae?eo ?icaeyiooi ?oo ca ?ia?oe??th
nenoaie aeaio o?e, ca’ycaieo ocaaaeueiaiei i?oaeiei oi?aa?naeueiei
oa?i??ii. Oeae oa?i??, e??i iaa?oaiiy iaaeiei eiai inae, i?eionea? i
cnoa a ieiuei? oa?i??o i aeicaiey?, e??i caeiieo, a?aoiaoaaoe i cnoai?
aeaoi?iaoe??.

Aaaaeaeinue, ui aioo?(oi( i?oaei( neee, ye( aeieeathoue i?e iaeeo
eooiaeo ( cnoaieo aeaoi?iaoe(yo, aecia/athoueny ianooiiith neeiaith
ooieoe((th:

aea

— a(aeiia(aeii aei?noeino( caeio ( cnoao;

— eooe iiai?ioo o(ea S2 a(aeiinii o(ea S1 iaaeiei inae oa?i(?o;

x,y — cnoa acaeiaae inae oa?i(?o;

o?ueiia e?aieaie iicia/ai( /eaie a(eueo aenieiai ii?yaeeo iaeino?.

sse aeyaeeinue, o?aooaaiiy cnoao i?eaiaeeoue aei iiyae iiaeo ?aciiainieo
/anoio ia?oiai ( ae?oaiai oeio.

Aeey ia?oiai oeio /anoio ciaeaeaii

I?e aea/aii( ?aciiainii( neooaoe(( ae?oaiai oeio iaeia ?aciiainia
oaeaee(noue aoea aecia/aia a yaiiio aeaeyae(

aea

a ?aooa ciaoiaeeoueny c ?(aiyiiy

(51)

Eiao(oe((ioe (51) oae(

A e(ioei oeueiai ioieoo anoaiiaeaii, ui ??aiii??ia iaa?oaiiy nenoaie c
iaeith ianeiao?i?th a ieie? ciaeaeaieo ia?oeo ?aciiainieo /anoio
iano?eea.

AENIIAEE

Io?eiaii iae?i?ei? ??aiyiiy ?ooo /ioe?ueio neii/aiiiii?ieo iaoai?/ieo
iiaeaeae: NCOO, ui ooai?ththoue iaiiacaieiaiee eaioetha; cae??ieai?
NCOO; iaa?euei? i a?euei? NCOO, ye? aeei?enoiaothoueny a?aeiia?aeii aeey
iiaeaethaaiiy noa?aeiy ?c caaeaiith o?a?eoi???th ?ooo a ?ia?oe?eiiio
i?inoi??; i?oaeii? eiinie?; noa?aeiy c iaeiei i?oaeii iaia?oei i
iaeiei a?eueiei e?ioeyie i noa?aeiy c aeaiia a?eueieie e?ioeyie.

ca(aathoueny c ??aiyiiyie iaeeo eieeaaiue i?oaeieo noa?aei?a.

Aeiaaaeaii ca?aei?noue ?ica’yce?a ??aiyiue ?ooo NCOO aei ?ica’yceo
a?aeiia?aeieo iaia?a?aieo a?aie/ieo caaea/.

Aecia/aii oiiae ?nioaaiiy a iaaaaii?e NCOO, yea ooai?th? iaiiacaieiaiee
eaioetha, ?aaoey?ii? i?aoean?? i anoaiiaeaii oi?io, yeo i?e oeueiio
i?eeia? i?oaeia e?i?y aaeo, yeee iiaeaeth?oueny c aeiiiiiaith oaei?
NCOO.

Aeine?aeaeaii oiiae no?eeino? a?eueii? NCOO, ui ciaoiaeeoueny a iie?
aa?iaeeiai?/ieo nee i iiiaio?a. Anoaiiaeaii ?ioa?aae aei?noeinoae; i?e
aei?noeino? c oeueiai ?ioa?aaeo ?oo aneiioioe/ii no?eeee o aeiaaeeo
aeinoaoiuei aaeeei? aei?noeino? (cie?aia i aeey iaeiiai o?ea) noa?
iano?eeei.

?ic?iaeaii aoaeoeaiee aeai?eoi ciaoiaeaeaiiy ?aciiainieo /anoio, a ieie?
yeeo noaoe?iia?iee ?oo ia’?eo?a c iaeith ianeiao?i?th iano?eeee.

Aea/aii iiaaae?ieo ?aciiainieo /anoio i?e ca?eueoaii? o?e a nenoai? i
anoaiiaeaii ?o ca?aei?noue aei ?aciiainieo /anoio i?oaeiiai ia’?eoo.

Aeine?aeaeaii aieea cnoaieo aeaoi?iaoe?e a i?oaeieo c/eaioaaiiyo.
Anoaiiaeaii iiyao iiaiai niaeo?o /anoio, ui c’yaeythoueny i?e a?aooaaii?
cnoao.

NIENIE ?IA?O, IIOAE?EIAAIEO II OAI? AeENA?OAOe??

Naa/aiei A.ss., Aiea?aaneay E.A., Eiiiiuoei A.A. Onoie/eainoue
aeaeaeaiey nenoai naycaiiuo oaa?aeuo oae. – Eeaa: Iaoe. aeoiea, 1991. –
166n.

Aiea?aaneay E.A., Eaiaoueaa A.I., Eiiiiuoei A.A., Naa/aiei A.ss.
Enneaaeiaaiea onoie/eainoe noaoeeiia?iuo aeaeaeaiee oaa?aeuo oae i?e
aicaeaenoaee aeaaaeainia ?acee/iie oece/aneie i?e?iaeu // Onoie/eainoue
aeaeaeaiey. – Iiaineae?ne: Iaoea NI, 1985. – N. 101-104.

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Eaa?aiaea, ia?acothueo iieocaieioooth oeaiue // O?. Iaaeaeoia?iaeiie
eiioa?aioeee «Iaoaiaoeea a eiaeono?ee». –Oaaai?ia. 1998. – N. 55–59.

AIIOAOe(ss

Aiea?aanueea (.I. Aeine(aeaeaiiy aeeiai(/ieo aeanoeainoae nenoai
ca(ycaieo oaa?aeeo o(e ( (o canoinoaaiiy aei aea/aiiy aeanoeainoae
noa?aeiaaeo eiino?oeoe(e. – ?oeiien.

Aeena?oaoe(y ia caeiaoooy iaoeiaiai nooiaiy aeieoi?a o(ceei-iaoaiaoe/ieo
iaoe ca niaoe(aeuei(noth 01.02.01 — oai?aoe/ia iaoai(ea. – ?inoeooo
i?eeeaaeii? iaoaiaoeee i iaoai?ee IAI Oe?a(ie, Aeiiaoeuee, 1999.

Aeena?oaoe(eia ?iaioa i?enay/aia noai?aiith iaoaiaoe/ii( iiaeae(
i?oaeiiai ia((eoo ia iniia( nenoaie oaa?aeeo o(e, c((aeiaieo i?oaeieie
oa?i(?aie; iaa?oiooaaiith aaeaeaaoiino( oe(e iiaeae( noa?aeiaai( iiaeae(
( aeine(aeaeaiith ?iai/eo ?aaeei(a ia((eoo c o?aooaaiiyi (o ianeiao?((.
Io?eiaii iae(i(ei( ?(aiyiiy /ioe?ueio ne(i/aiiii(?ieo iiaeaeae.
Aecia/aii cia/aiiy aei?noeino( i?oaeiiai oa?i(?o, yea caaacia/o( ca(a
?(aiyiue ?ooo ne(i/aiiii(?ieo nenoai i?e iaiaiaaeaiiio ca(eueoaii( /enea
o(e a ieo c ?(aiyiiyie iaeeo eieeaaiue i?oaeieo noa?aei(a. Aeiaaaeaii
ca(aei(noue ?ica(yce(a ?(aiyiue ?ooo aeene?aoieo iiaeaeae aei ?ica(yceo
a(aeiia(aeieo iaia?a?aieo a?aie/ieo caaea/. ?ic?iaeaii aoaeoeaiee
aeai?eoi aecia/aiiy ?aciiainieo /anoio, a ieie( yeeo noaoe(iia?i( ?ooe
ia((eo(a c iaeith ianeiao?((th iano(ee(.

Eeth/ia( neiaa: nenoaia ca(ycaieo oaa?aeeo o(e, i?oaeiee noa?aeaiue,
i?oaeiee oa?i(?, aei?noe(noue, ?aciiainia /anoioa, no(ee(noue.

AIIIOAOeEss

Aiea?aaneay E.A. Enneaaeiaaiea aeeiaie/aneeo naienoa nenoai naycaiiuo
oaa?aeuo oae e eo i?eeiaeaiea e eco/aieth naienoa noa?aeiaauo
eiino?oeoeee. – ?oeiienue.

Aeenna?oaoeey ia nieneaiea o/aiie noaiaie aeieoi?a
oeceei-iaoaiaoe/aneeo iaoe ii niaoeeaeueiinoe 01.02.01 – oai?aoe/aneay
iaoaieea. – Einoeooo i?eeeaaeiie iaoaiaoeee e iaoaieee IAI Oe?aeiu,
Aeiiaoee, 1999.

Aeenna?oaoeeiiiay ?aaioa iinayuaia nicaeaieth iaoaiaoe/aneie iiaeaee
oi?oaiai iauaeoa ia iniiaa nenoaiu oaa?aeuo oae, niaaeeiaiiuo oi?oaeie
oa?ie?aie; iainiiaaieth aaeaeaaoiinoe yoie iiaeaee noa?aeiaaie iiaeaee e
enneaaeiaaieth ?aai/eo ?aaeeiia iauaeoa n o/aoii aai ianeiiao?ee.

Iieo/aiu iaeeiaeiua o?aaiaiey aeaeaeaiey /aou?ao iaoaie/aneeo iiaeaeae:
nenoaiu naycaiiuo oaa?aeuo oae (NNOO), ia?acothuae iieocaieioooth
oeaiue, cae?aieaiiie NNOO, ianaiaiaeiie e naiaiaeiie NNOO. Onoaiiaeaii
iaee/ea o aaaaeaiiuo nenoai ?aaeeia, a eioi?ii nenoaia naycaiiuo oae eae
iaeii oeaeia a?auaaony aie?oa iaiiaeaeaeiie ine. Caienaiu o?aaiaiey
aeaeaeaiey eco/aaiuo nenoai, eeiaa?eciaaiiua a ie?anoiinoe ?aoaiey
niioaaonoaothuaai yoiio ?aaeeio.

Eco/aiu o?aaiaiey aeaeaeaiey nenoai i?e iaia?aie/aiiii oaaee/aiee oae a
nenoaia e iaeaeai eiyooeoeeaio aeanoeinoe oi?oaiai oa?ie?a, i?e eioi?ii
aaaaeaiiua eiia/iiia?iua iiaeaee a i?aaeaea iienuaatho iaeua eieaaaiey
oi?oaeo a?auathueony noa?aeiae.

Enneaaeiaai /anoioiue niaeo? naiaiaeiie nenoaiu naycaiiuo oaa?aeuo oae,
aeanoeinoue oi?oaiai oa?ie?a a eioi?ie auea aua?aia ii?aaeaeaiiui auoa
ia?acii, e onoaiiaeaia aai noiaeeiinoue e /anoioai oi?oaiai noa?aeiy n
aeaoiy naiaiaeiuie eiioeaie.

Onoaiiaeaii niioaaonoaea iieo/aiiuo o?aaiaiee i?aaeeiaeaiiie
iaoaiaoe/aneie iiaeaee oi?oaiai iauaeoa n iaeiie ec aiciiaeiuo oi?i
?aciinoiie noaiu ii i?ino?ainoaaiiie ia?aiaiiie o?aaiaiee a /anoiuo
i?iecaiaeiuo, iienuaathueo eieaaaiea oi?oaeo noa?aeiae. Yoi iicaieeei
eniieueciaaoue oai?aiu ?aciinoiuo noai aeey aeieacaoaeuenoaa noiaeeiinoe
?aoaiee eco/aaiuo aeene?aoiuo caaea/ e ?aoaieyi iai?a?uaiuo.

I?eiaiaiea iaoiaeia aiaeeoe/aneie iaoaieee i?e eco/aiee aeaeaeaiey
oi?oaeo iauaeoia i?iaeaiiino?e?iaaii ia i?eia?a aeieacaoaeuenoaa
nouanoaiaaiey o NNOO noaoeeiia?iuo aeaeaeaiee e enneaaeiaaiey eo
onoie/eainoe.

Aiaeec oneiaee nouanoaiaaiey i?aoeanneiiiuo aeaeaeaiee o NNOO,
ia?acothueo iieocaieioooth oeaiue, i?iaaaeai aeey neo/aaa, eiaaea oaea
naycaiu noa?e/aneeie eeai oieaa?naeueiuie oa?ie?aie. Iieo/aiu oneiaey
nouanoaiaaiey oaeeo aeaeaeaiee e onoaiiaeaia oi?ia, eioi?oth i?e yoii
i?eieiaao oi?oaay eeiey aaea, iiaeaee?oaiiai n iiiiuueth nenoaiu
naycaiiuo oaa?aeuo oae.

Aeey eco/aiey iiaaaeaiey oi?oaiai iauaeoa a iiea ay?iaeeiaie/aneeo nee
e iiiaioia ?anniio?aia caaea/a, a eioi?ie oi?oaee iauaeo iiaeaee?oaony
nenoaiie aeaoo ae?ineiiia Eaa?aiaea, naycaiiuo oi?oaei oieaa?naeueiui
oa?ie?ii. Onoaiiaeaiu niioiioaiey iaaeaeo ia?aiao?aie nenoaiu,
oa?aeoa?ecothueie aeaenoaothuaa neeiaia iiea, iicaieythueie ae
niaa?oaoue aeaeaeaiea, a eioi?ii oeaio? iann nenoaiu aeaeaeaony
?aaiiia?ii e i?yiieeiaeii e iia a?auaaony eae iaeii oaa?aeia oaei aie?oa
ine, eieeeiaa?iie aaeoi?o nei?inoe oeaio?a iann. I?iaaaeaiu
enneaaeiaaiey yoiai aeaeaeaiey aeey NNOO, iaoiaeyuaeny iiae aeaenoaeai
noiia?iiai ainnoaiaaeeaathuaai iiiaioa.

I?e eco/aiee ?aaiiia?iuo a?auaiee aie?oa aa?oeeaee ianaiaiaeiie nenoaiu
aeaoo ae?ineiiia Eaa?aiaea, naycaiiuo oi?oaei oieaa?naeueiui oa?ie?ii,
onoaiiaeaiu niioiioaiey iaaeaeo aeanoeinoyie oieaa?naeueiiai oa?ie?a e
noa?e/aneiai oa?ie?a oi/ee cae?aieaiey, i?e eioi?uo iaiaoiaeeiua oneiaey
onoie/eainoe ?aaiiia?iuo a?auaiee auiieiaiu i?e ethaie nei?inoe
a?auaiey.

Ii?aaeaeaiu /anoiou, a ie?anoiinoe eioi?uo iiyaeaiea iaeiai aeaaaeaina
i?eaiaeeo e aicieeiiaaieth a eo ie?anoiinoe cii iaonoie/eainoe
noaoeeiia?iiai ?aaeeia. Yoe /anoiou auee iacaaiu ?aciiainiuie e
onoaiiaeaii, /oi iie yaeythony e?aoiuie ei?iyie oa?aeoa?enoe/aneiai
o?aaiaiey, niioaaonoaothuaai neiiao?e/iie nenoaia. ?aoaiea /anoiuo
caaea/ i?eaaei e iino?iaieth iauaai aeai?eoia iaoiaeaeaiey ?aciiainiuo
/anoio eae e?aoiuo ei?iae oa?aeoa?enoe/aneeo o?aaiaiee, iieo/aiiuo i?e
eco/aiee neiiao?e/iuo nenoai, a caoai eieaeueiiai enneaaeiaaiey
ie?anoiinoe yoeo /anoio aeey nenoai n iaeie ianeiiao?eae.

I?iaeaiiino?e?iaaii i?eiaiaiea yoiai aeai?eoia ia i?eia?a enneaaeiaaiey
?aaiiia?iuo a?auaiee nenoaiu n oae, aeaeaeouaeny ii eia?oeee. Auaeaeaii
aeaa oeia ?aciiainiuo /anoio e i?aaeeiaeai aeai?eoi eo iaoiaeaeaiey.
Onoaiiaeaia noiaeeiinoue ?aciiainiuo /anoio aeene?aoiie iiaeaee e
/anoioai oi?oaiai noa?aeiy.

Eco/aii aeeyiea neeiaiai iiey e naeaeaiauo aeaoi?iaoeee ia aaee/eio e
eiee/anoai ?aciiainiuo /anoio.

Eeth/aaua neiaa: nenoaia naycaiiuo oaa?aeuo oae; oi?oaee noa?aeaiue;
oi?oaee oa?ie?; aeanoeinoue; ?aciiainiay /anoioa; onoie/eainoue.

ABSTRACT

Bolgrabska I.A. The investigation of dynamical properties of
interconnected rigid bodies systems with application to studying
properties of rod constructions. — Manuskript.

Thesis for a doctor’s degree by speciality 01.02.01 — theoretical
mechanics. — Institute of Applied Mathematics and Machanics of NAS of
Ukrain, Donetsk, 1999.

The dissertation is devoted to creatign the mathematical models of
elastic object as the system of rigid bodies, interconnected by elastic
hinges. The justification of adequacy of such a model to elastic one,
and investigation of working modes of the object by taking into account
its asymmetry are developted as well.

The non-linear equations of four finite-dimensional models are obtained.
Such value of stiffness of an elastic hinge is found that the motion
equations of finite-dimensional systems with unlimited increasing of the
number of bodies are coincided with the equations of small oscillations
of elastic rods.

The convergence of solutions of the motion equations of discrete models
to solutions of corresponding continuous boundary value problems is
proved. The effective algorithm is developed for determination of the
resonance frequences, i.e. frequences in the neighborhood of which the
stationary motion of the objects with small asymmetry is unstable.

Key words: interconnected rigid bodies system; elastic rod; elastic
hinge; stiffness; resonance frequency; stability.

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