clanci o raskovicu - katica hedrih

7/25/2019 Clanci o Raskovicu - Katica Hedrih

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LANCI

Prof. dr Katice Hedrih

o Prof. dr Danilu Rakoviu(sa bibliografijom)

Priredili: Prof dr. arko Mijajlovi Dr Slavia Milisavljevi

Beograd, 2014VirtualLibraryofFacu

ltyofMathematics-UniversityofB

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Projekat OI 174001 Dinamika hibridnih sistema sloenih struktura 2011-2014)

Serija predavanja za istraivae pripravnike i doktorante iz oblasti Kinetike,

Elastodinamike, Analitike mehanike, Primene tenzorskog rauna u mehanici, Teorije

oscilacija i Nelinearne dinamike

31-vi blok predavanja

od 11h do 13h) i od 15 h do 17 h)

Osnovi tenzorskog ra

una sa primenama u mehanici

Transformacije, ortogonalna, afina i opta transformacija; invarijante; kovarijantni i kontravarijantni

vektori i tenzori; kriterijumi za odreivanje tenzorske prirode sistema; kovarijantne, kontravarijantne i

fizike koordinate vektora i tenzora; Christoffel-ovi simboli; kovarijantno diferenciranje tenzora;

diferencijalni operatori; bazni vektori tangentnog prostora vektora poloaja materijalne take i ugaone

brzine njihove rotacije; Primene tenzprskog rauna u analitikoj mehanici mehanikih sistema; primena

tenzorskog rauna u teoriji elastinosti;

Drugi de0)

Predava

Prof. dr Katica Stevanovi) Hedrih,,

rukovodilac projekta OI 174001

Sreda, 22 februar 2012 u 11 asova

* * * * * *

Predavanja se odravaju svake srede od 11 do 17 asova u Biblioteci Matematikog instiuta SANU, ul.

Knez Muhalova 36, trei sprat

Prijava potencijalnog sluaoca se dostavlja Upravniku Odeljenja za mehaniku na adrsu

[email protected] sa naznakom oblasti interesovanja.

Dr Sran Jovi Prof. dr Katica Stevanovi) Hedrih

Sekretar Odeljenja za mehaniku Upravnik Odeljenja za mehaniku

VirtualLibraryofFacu


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* . ,

, , 1952,* . ,

, 1972

, 1985.

Prof. dr Ing. Dipl. Math. .



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100

,

oeoDr Ing. Dipl. Math. ao . ao28. 1910-29.1985)

aa (eao) e



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ao . ao28. 1910-29.1985)



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EOO

"oo ao e o, a oa eaa o."

JoaJoaoaj

, ,

.

, , . -

. ,

, (, , ),

, . ,

. .

. .

.

* * *

eoj a aoo ooa , jeo ea ee, eaee oo ea, oeo

eae eo aa e aa, oe eaaa eoje oaja oaoeae aeoae ee oe e, ee, oea oaoaa Ojaa. eoe eee oa aoaooa oae o a a e. eoaj je o , ao ajoajoeoaaa, oea.

ao oa aa aje, oeo ao je ea eaao o oajaa e, o ajaojeejaoj jea a a oe oa, oe eejaa, oajaa oa ooaa. ooo je o ea oajaa oeeeja oje , , oo. aa a e e oaje e oe o oaee e, j eoe aeoae e.

eoja oaja je a oeooa oea aa oaojoj jeao aao, ao oj oo.Jeaaeo ee oae ooe aoje oao oj aao oae ooe ea, oeoeoj eaoeoj oaja, a eoa ajaa e, eoa ea e, je a oj oaa aaa eo a o oajaa, o ee aa a eeeoeoa.

aa aooeeoaea , a oeoa aoa je o eoa aooa,je je oe eao aae a oja e aao oj e eo eaaa, a oja je ooaaao, o je ooo a aaeeeeej, oj ao-eaoaa ea, oeja e aoa oaa ae eee a eajoeoaa o a. o je eo oe oaa ojeaoa aee a eaa aoaeeoa, o je oeo o aeea aje eoooeoa eae a oae. a aoaeeoaoeoaoje o eaee a ea, a a aaa oea. eeao, , 2000. o,eeaoa oe, a eaOeea a eaaeaoa Aoeeo50. oaje e a eaa aeaoae, o jao , o jeooeoaeae aoaea eoaoe"a je oeoaoao aaje eeee aaaoaeae" a oae, a o "e ea a e aeaeo, jeje aajo oeo aeaae eae, ". oe je oooo. Joo o.



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oeaje aoaea eoaa aao eee oae: aejea: eoo: a, ea, aja, ee, a e o eao.aoe ao ooje oa a aooeooe ooe: aja (1912) a e:a (1940), jaa (1944) e (1946). a ae: "a oj e eao a ajeooo?" oooo je: a aaoje aa, ae, a e aaaoa oj, oooo je: eoja eaoeaa.

1951 o, eee . 16578 o 1 aa 1951. oje e oaee aaaoa a ooajoeaa aoaea. oeea o25 ja 1958. oe ea je aa o a ooajoeaa aea ea aee a o-aeae ae.

eo ooe 1963/64. o 1973/74. oe o je eaee a eaaooea eoaea , a oeeo ao aaeea e a ea.oeo, je ao aaeae a eaea ajeoa, ao jeoeoaaeee aeae a oo-aeaoaeooa. , .. 67/8 1964. . [*].

1974/75 . , I, . , 1985., .

o je, , 29. jaaa 1985. oe eoa.oeoao ao je oOoae aae aa a, a ooe a

ee, o ee ajeeaa oje oe oejeaa.

a* *

a 1.oeoaoa oeaa (*) (*) (, . , -).

eoaeja: 503 294, oj: 47213, ae oae ao e, a aa aa ea aoaea . O, oj je dipl. Math.ao ao oo 9. eea 1946. oe oj aoooao aaa ee

ooaje eaoeaaeee oae: o oje 12 a ae: "a oj e eao a aje ooo?"

oooo je: a aaoje aa.a ae, a e a aaoa oj, oooo je: eoja eao

eaa.

a ae o 16. ee O aao je ooo: 1941 a ao ee a. Oo a aaa, aaeoeaa.

ooa oaj. aoje ojeo ao eee:oeea, aaja a, a eo, ea ooa ea oa

eoa (j o e ao . . eao). oe o oa, a ja aojeaaeoee. oeeoooa, , o aeooaa. a oeoao aeaeaje



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a* *

a 2.oeoaoa oeaa a aoea: eaoa a eaAae1958. (a*) eaoaoeeja eeae oaje ICNO e1968 (*).

oeo je a je ooa oaao, e eaee, oaeeejae jeae "ja aoa" a aoaoee, a e e je oje je oaao ee eoje eao, oeo a oa jaa a ee. eeae jeje aao ao oeeoje eao.

:ao-eooo oo aeee aae eae; eoja eao; eoja

oaja; Aaoje oea; ae eo. , ZentralBlatt-.

*eoja eao.ae ooe oaeoje eao. je ao oojooe

oae 1944, 1947, 1948, 1949. Aa e je ao o eea jeeeejae jeae, oja e e oe e aoeo o je je eee aaoeo eaoo eoo. je aoa aa aoaoo oeo eea, oj jeoeeea ajae, je e aee aoj aoaaja aeaejaaoa.

aaeeoeo aaejaa (Hubert-Hencky) ea ojoj je ejaoaaaoa aa eoaja ea e eoaja oeo oa, . ao jeeo eeejaoa oejaa eaoea jaoo.

eo je ooe jeae eao eoo o ao je o oaaoa ooeoa jaa je eo Beltrami-jee jeae oaoo.

ao je ooaaejeoaea je ajaa ee aoaoooeoeea. oo je oe Briot-Bouquet-ooeoo, oooe ee oaao a je aaeea x=a , z=0 eejaae eaa eejae jeae ja aejaoaoa ee aoaoooeoeea, oeeee a ajae.

* eoja oaja.ajeoj oaaoa . aoa je oaeoje oaja (o1953., 1954.,

1956., aae oe o jeaoaao 1966.).ejeojeaa oaaa a aj ojoaja aa a e

oa, oao je eaaooa Clapeyron-oo"jeaojoeaa", oja e oeea eaae aaaa ojoaja ooeaa. a ae ae oeeo je eee jeae aeeo o oeo oee e eejeooaa.

aao je a ee ae ooe oejeaa ee ooa. eo je

eee oe a eee jeae, ao ooeje eaje oaao ooLagrange-oe oe aoe oe aa ja.oaooae oaje oeaoeaa ojaeaa, aoo je

oeaoaja aoea aoo. oaao je a e aoajaa aaaoa oea oeeoa, a ooNewton-oe eoe oeo ae a oeeeo. eo je oaaa o oa oaja eooejeaja.



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aeeoa, oooaeooa, Eeooaea ojojo-eoj oeoa. eaoao ao-aaoao. . . oe a e eea eoa . 75 o 1957. oe, aao ooo aaooa a eoo oeoa a ea. ea ea aaea ee ao, o.aoje o eooaaaa a a aeaoooaea ooao je aaoaa eeeea aeaa.

a aooeeoaea , aje a aoae,ao je aa a oo jaa : Aaa eaa, eojaeea oaja eaa oa. o je e aee a ea aoa

ao aea . o je eo aa oeo, a aa, oj je ooeoeaa, a aaaoojoea ooaea, ao eea ae, jeje eoa oee eojaoaeaa.

a 3. oeoao, .

, .

oe oa ae eoooeoa o. ao je ao eo a ojaaeeea eea, oje je eaao, ao a oaa eeaja ea oj oaa ooea aa. o ea eeaa, oe e oaoaa oaaaaoaaa. oooa oaaeae oe oaa eaa ee aeae, a a oeeo aa e a ooaaj e



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ea. eoa eaaa a "aeaa oea" "eaa a eee ee","aeao aae oje" ao eeoaeoae oaeoaeaaa ee. aaao je eoooa oaa oeeejoeaee a , oja eeeoea.

eoee a eoa eaaa, jeao a.a aa, ea eaa I (aa) ojaea "ae e" o

a o 18.000 eaa. a oaa: Oo eooaaa - eoaaea. oo 40.000 eaa.

a a aa ea eaa II (eaa) a o 13.000 eaa.ao e oeo eaae eaoea, e je, ao e: "oao eeae oee, a eo o aao ao eaa, oje e o ao oo aoaae eae eaaa." eoaa, eeoa eejaoj eoej eojoa. oo aaeae ee oe ojae: 1* ooee eoa aa oj ooa ea: oao-o eo e ooaa, ao eeaao e ooaa, a aoe oe ooee eoa aa, a ooaajea; 2*Euler-oe oe oaa eaoo eoe oe; 3* eaa; 4* oKardana Hook-a. ooj oao je oeaLorentz-oooeeaaeoea.

a 4. ao, , ,

. ,

.

a a aa, 1947-48. 1956. oe ea eaa III (aa) ojaea oao10.000 eaa. eea aa aa ae eo1962., 1972., 1973.o. a a je oo 19.000. eaa. ao oa oo, ee e : Oo



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eoje oejaa, oeeje eaa o. eejoea eae oa aaa oaa aeae, Oo ajaooaa.eo a 1972. ea eaa III (aa) "oeaea aea", oaoje ooa oajae oaajae jeae eaa.

eeeee, Oooaejaa oeo je aa 1954. 1984.oaoo 25.000 eaa.

ae Ooo aejaa aaj e, 1961. , ao a e a eeaoaea eoa. 13 aa oe e oaa o 40.000 eaa.

o eaeo o aa ea eoja oaja je ooeo ao oao

ea: "Treatise on Natiral Philosophy" jooajaa:Lord Kelvin-a Peter Gutrie Tatt-a: "Neitherseeking nor avoiding mathematical exercitations we enter into problems with a view to possible usefulness for

physical sciences ". aaaaj, e 1953 oe, a e oeoj e e e ajeaoaoe, eajooeo je o eea e ojaee, aoa a a ae jea oaaja, o o aaj aeeoaeao ee oja je aee, eo ee eaea, ao e eee. aa, oaj eje oo eoa oeaaj. oeo aoooo aoeo, a je aaj ooea aa, oe oo oa ea, aee, oe, o aaao oeeaeaaaa.

a Ooaoaaaojaea je aaoj aa a, eoa, 1971. aaa je oooo: "Mathematik ist die Kunst Rechnungen zu vermeiden". . aoeooooea e: "ao aae e e oe ae ee e: eojoaja,eojeaaa, aoja, eeoe, aoaeae. ooa e a

oeaea oeoaa oe ooooaaa, oje aooaa oea oo oaaa ea oee aaa". ooaooe ee e aeae a ee aaea, a eoea o jea oaa: Oo eooaa Oo eoje je oee oee aeoooooaaa oaeaaaaoaoea eoje eaoeae eeea, o je aao a je, a aa je, oo aeea.

eOoeoje eaaa, ojao je aoa aae ea , eoa, 1965. ao2000. eaa. Oaj eaeaaa oja je ao ea ooeea ea ea oo-aeao aea eoa, a je o aaj o eaaaea, ojaooa. o aaaa o je jeaoea aoaaajea aeje.

oo eAaa eaa, ojaee 1974. oe, oeoaoje oajo oJ. .Lagrange-a eoe oae ooaje "Mecanique Analytique" 1788. "...Oaj oj o Aaae a aoooa je oa eeo e aaa, o aa aj aoo eoe...". aaj oe e je oaao a oeoja oj je oeoaoao a ao ae aje, a je oo ao a oaea aaaaa ooaajea a oeo jaa ee eae a aooeeoaea , aje, aajeoa, oje je a jaa ao.

o. ao je aao ej aaaa eae oje oae aooaajea.

e oeoa aa . AOA ea oao oaaa eaooe ooe aae a a aea j Joaj, ao aoo-aeaaea eoaooa.

O aj ee ea e eae oeoa aoa ajojeoo ao ee, oj je oao a ao

aeeoa, a aoo e oj eea: ee oee aajooeeo,jeaeo oeoea aejaa ooeea oaejee oe eeaeaae; a o je o oeo ao oje ae oje a ao e aa a oeaa ea Oooaejaa oaoa ooeoa aa aoa".



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a 5.oeoao()

. -.() : : . ,

)

EOEO OEO AO

eee, ae oeo oa ooe, oa eao .oa Oao, aje aaeA, eea 1957. oe : "...aao je oeoao-ee ae, eoo a eae, aeae, Oooaejaa aee eae oe ee eae, Ooo aejaa eoje oaja aee eaea eee. eeoeeoo aa". a ea a a aoa a ooaaj a ao eaa. a aj eaj:"....aao a aajao oao-ae ae, oje je aa ojao aaoa. oao o ae31 a22 e. eo a ooao eoe o ooaaa ao aoaa, aa aaa. aoj oa ojo e ao, oao je

aae. a- ao e ao oa oaj eea- aae e a e aaaaaoeeeoa. aa je eo aaaa ae oe, a aaa oaoeoa, a je eo a ao ao ee oeo ooj ea, oa, a, ojoj. o je a eea aoeoj ooaaa a aao, oja ao a ao a o aa ooae, a aojao a aj a, aoa a a aea, a oe eeooa aa eaaoee eoe aaaaa ae ee.... . . ao je oa aaeao. e oaaoje eee e aao je ee eea, oje je eaao e e ooeeojaoa...".

. ao je o o oaa oe ao je aa aj a aoj ae oooe aae a ee. eoo o o je aaeo a. Oaoje oje oae ojea "e aje" oao eoeaa.

oeoaoaea ajeaoeoa eea aje

ojoj oeo, o oeoao, eoao, e:"aa, a, ooo je a oao a e eee a aeeoooje eoje oe. o je o aeo o e, je e aje oj eea oj e aa aa aea o a oeee eoe e... oo oaae aeae...Oeaa je ao ae. oea je o aea...ao je o, a o eaaeo, ajee oeoa eooa......oaao je eo ee a eaa. je ao aao ae,oaaj ae a ae.... A e eaa je oaao ae: "a ee aooaae a eoe?"

Oeo ea a, oj ae oea, oj je aao , ja ee, ao je oao ea ea, aooe aaaa. aea, oje aja ee



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ojoj a, eaaa e aaa eoo aea,eee ea oa. oeoa aoa je ao oo aaaeeeje, ojoa je oa oaa, o je ooo oe -, eaoejaoeeo. a . aj , o, oe. oojaeo oeo a ojea aao aooa. o oao, ooeeaa, .

o aa oe oj e eo aa a o ooa.

, , oe o oa e aea, oje e, eeo oaaa a e aaa, a aao, a o eajoeoaoeea. eoa aoeaaea ea, eoa aa oaeja aa oeje ee, aao aea aaa a a ae ejaa aa, o oo aa,oeoaa aa.

ao ao je o aa eea eaa, a aeaaa aa, Socit mathematique de France, Geselschaft fr Angevandte Mathematik und Mechanik (GAMM) eaa,aa aeao a A ao a A, eee aoa AppliedMechanics Reviews USA, Mathematical Reviews USA, Zentralblatt fr Mathematik und Grenzgebiete Berlin eeaoaa eaa oa.

eae ooo oeoa aoa eo 1974-75. oe. o a aeaaa, a eajeoaoa, aeje a ea, ao o aoe ooe aa.ea je a oe aa oaoa eoo o, oea ojje oao oaeoe, oj je e oj aaa oe oa, ae a o oeeoeoja eao, ao, aoeao: "ao aaaeae ee ee aoaoae aoea. ooo aao a, jeo aoo aoo oeo. aa

e e". oa oa je a a ee. je a jeaa a ea a oeo, oeae oja je ea. a ee ee, ao , oeaaa.

ao je oeo eeje o oaa o. aa aoa, o je a eea oeeaja eaa, ao eeea ojo, eeea, ojeo ooe o eo aaa a aoj aooaa aoa eaa e oaaa, oae oeeaja eeoeoa. oeeajaa eaa, oj ooeoa AOA , aoeea, aoa a ae ee, ao o eaaa, ao o e o 140.000 eaa aea aaaa, oao je .a a ao oe eo aea , a oeoa aoa je o eoaaooa, je je oe eao aae a oja e aa, , o jeooo a aa e ee eej, oj ao-eao a a ea, oe ja e aoa oaa ae eee a eaj o eoaa o a. eao, 2000.o, eea oa oe, a ea Oeea a ea aeao a Aoeeo50. oa je e a eaa aeaoaeo jao ,ojeooeoa eae aoaea eoaoe"a je oeoaoaoaaje eeee aaa oaeae" a oae, a o "e ea a eaeaeo, je je aajo oeo aeaae eae, ".

EE AA AOAAAEAOA AEOA

a o , 1946 o, eoe e aaeje aa o 26 aa 1946. oeooeje aaeaoa A, e je ooa. a eoo15. aja 1946.oe aeaA je oeo a aao aa ja A-a. Aae Aooje o a, a oaoj aaeeaa.



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a 431. eea , o26. ooa 1960. oe, ao 578. aoee, o je aoeoeaeo aoee oo, oao: "ee ooe jee ae ooa oeeoo eja Jaccobi-je aa" (16). oae o jeo ooeo ojo ea aoj a eaa aa, j je oo aeao eee oaa eeejaa jeaa ooaa ea ao o. eoaaj eee eoejao o, eo je aae jea oo oaoo oea. Oa jeaea oo jeae ejae Jaccobi-jee ae. oaao je a a e ooe aee oa, e je oeo aja eea. e oa oeje ooaoajjaoae oe ojea oee, -aa.

a oj e, ao 579. aoee , oaoa . Joaoeaoe je aoao: "O jeoj aLageur-oooa" (17). oaa je oaoeoje aojoe aeaaa a aa (oaa). ooLageur-oeejajeaae e aae je e eeja jeaa o ea ao o ooaaja aaea jeaa ooaooaoooaa eaoea. Oo je ee ooee aaee o ooa, oe ee oae ao ae ooejeaa.

a 6.oeoao

aoea o. . aoa a eaa ooooaOeea a eaeea:(1962.) O oja eeae oaje aa ICNO 17-25. eea 1962.; (1963.) aeoaje aoaoaa a oja aaee oeae ae eae oaa; (1963.)O jeoeeaoeaoe; (1963.) O aoea; (1963.) eeao eojoee: Optimization technique Edited by G. Leitmann.

aoe je 27 eea 1963. oo aoao: oejee ae aaojea oee ao ajao o oaa a ea ooa. a oj eaao je aaj eja: Sability by Liapunov's Direct Method with Applications, J. La Salle and S.Lefschetz eoeaoaoA. oea.



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Hochschule Aachen. aa e aoaao o aa aoja aaaa oaeae oaeoje aa eaaa, ao o eeoj aa oe oa. o ooooe je aaj aaa, jeoaaa ao oea eoaea ooa a aaa a oj ooj o Aachenu. ea o ao"Lagerschwingungen bei sphrischen Getrieben" je aea oaea, , 1970, ooooaa a ao oe eo aea . ee oje aoajoe o je o. ao ao.

a 7.oeoaoa , (1973 )

OOAOJEEE AE

a Oa eaaa"ee e" aaa je 1950 oe, ao 7.000.eaa, eae a 79. ooajea oea je 27. oaaoa, aao eoo oaeae o aoa a aoa (1935), . Aoea (1947), A.oa (1948), ao oja eea ea eae oaa eoo 1947o 1949. oe.

Oaeeeee oaaoa : . Oaoa Ooae o ja(1937), . JaoaOoao eeea (1948), aaoooooe (1936, 1941), . aaeee (1948), . ae eooa a (1938), . ajoa aoea (1946), .oooa eaj e (1947), . ja eaoo (1948), J. eoa oaae (1948), .Jooa ae (191948), . eea oee a (1935), . ooa Eeeaaa, A. eoa ae ae (1933), J. ea eaa a ae (1949), o-o. aee (1934). O aoo eae oa e aa oa aoa a aooeae oaaoa.

oa ae o"oeaoee a jeooaoeeeaoooeoeao, oja a aa ee aoa, jeaaaojee aea oeoe e ee oe.". o e. aoa: "ea eooeo aa, aaeo oe oaoa ao ojea". aaj e je eo oea, je oaa:

ooe ojoe aeee e, a, ea, aoeaaeoa.a je aaa " eo" "o" a "aaea aaao", a je"o a aja ao ae ao e, a e aea oa oaaa".aoe oaeee"oeoeaa eojoaaa a ao" ao ae "aa oe aa oe e o oo ae a ojee oje eaaa".oao je a je ae oae e "eo eao, jea jee ae eaeaaaae, a a e oaaoja aaea". o je aa oe eo. aao je "e", a je oaea o e, aeoa je aa aa aa a ae, ao je aeea aaa eaoa. eo e a aaj, a oeo eoao eoj eeeeeaa eae. aa je o oaajjeea oe oa.



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O aj ee ea e eae oeoa aoa ajojeoo eae oeoa . ja a je aoaaj a je ao eeo, oj jeoao a aoaeeoa, a aoo e oj eeao eeoe:ee oee aajooeeo, jeaeo oeoea aejaa ooeea oae jee oe eeae aae; a o je o oeo ao oje ae ojea ao e aa a oe aa ea Oooaejaa o aoa ooeoa aa aoa".

a oooa je ao: Ao je ooea aa e aoee e jeo, oeooao e ao aea o ooo a a eaa ae oe

eoeaooo, aaeooaojoje ee oaojaeoaee aeea eeaja aj a eeo o oeoa aa aoa. O oaje oao a oojooeoaoaoaoeea oje ooaa a aeoooaj ee ae ae: a je eao oooa . , , oa, .

a 8. oeoao, () ,20. 1984, ,

, 29.1985.

EO

e: 128450, aeea ooaja aoaa e oe a a.O oa, eea oea. Oo oea, oja ao. aa e o oe



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. : a je o aaeeoaeoa aea a eaOoooja oaoo.aa aoa a oaea?

oo a aea eee oaeae j ae eae a eea a eoaa, a e je oeo ao aoao oeoaa a aoaea eoa, , , . eoa jaeeae , oaajea.

eae ooo oeoa aoa eo 1974-75. oe. o a a

eaaa, a eajeoaoa, aeje a ea, ao o aoe ooe aa.ea je a oe aa oaoa eoo o, oea ojje oao oae oe, oj je e oj aaa oe oa, aea ooeeoeoja eao, ao, aoeao: "ao a aaeae eeee a oaoae aoea. ooo a ao a, jeo a oo aoo oeo.a a e e". oa oa je a a ee. je a jeaa a ea aoeo, oeae oja je ea. a ee ee, ao, oeaaa.

ao je oeo e o eeje o o oaa o. aa aoa, o je aeea oeeaja eaa, ao eeea ojo, eeea, ojeo ooe o eo aaa a aoj aooaa aoa eaa e oaaa, oaoeeaja eeoeoa. O je

eao ea oajajoaojaoa, oo oa, oe ooooaaa eea, a oeo je oo e eeje.

Oeo je a je ao . ao o a ee oeo aaa,ee aaae eeje, aaoejaa, ojje o eaooaeo aeaeaooeaea, ao je oao oee eae, oje oe aeoejaa aea oea, oee oao, a o je oao oe e ao. oeeajaa eaa, oj ooeoa AOA , aoeea, aoa a ae ee, ao o eaaa, ao o e o 140.000 eaa aea aaaa, oao je .

Ao oo ea oao je e ae oeoaa a, oj oj oeaaaj oea aa oeoo ea a. Jea o ajaej aaaoeooa je aao aEeoje e, oj je jeo ee oeo aooao ea a ooa aoaaoj a aoao o ojoj oeojoeaoeea a, oje je eo a ooa oee aa.

LITERATURA

1. Hedrih (Stevanovi) K. i StudoviM., Profesor Danilo P. Rakovi(1910-1985), Biobiliografija,poglavlje u knjizi: ivot i delo srpskih naunika, urednik akademik Vladan Djordjevi, Srpska Akademijanauka i Umetnosti, Biografije i bibliografije, knjiga X, Beograd 2003, pp. 239-270,..

2. 1946-1961. Matematika i Mehanika, Beograd 1990. Priredio Milan P. ^av~i}.

3. Referatod 20 maja 1957. godine.4. Referat 1517/2 od 17 februara 1956. godine.

4. Slu`beni~ki list br.128450 dr Danila Ra{kovi}a

5. Personalni list serija: 503 294, broj: 47213, dr Danila Ra{kovi}a

6. Arhivska dokumenta Ma{inskog fakulteta u Beogradu - fascikla dr Danilo Ra{kovi}

7. Autobiografija dr Danila P. Ra{kovi}a iz 1952. godine.

8. Predgovoriiz univerzitetskih uxbenika Danila P. Ra{kovi}a iz prvih i ponovqenih izdawa.



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9. In Memory of Professor dr ing. Dipl. Math. Danilo P. Ra{kovi}, Professor of the Faculties of Mechanical Engineering inBelgrade, Ni{, Kragujevac, Mostar and Novi Sad,by Katica (Stevanovi}) Hedrih, Facta UNIVERSITATIS, Series Mechanics,Automatic Control and Robotics, University of Ni{, Vol. 1. No. 4, 1994.,pp. VI-IX.

10. Katica (Stevanovi}) Hedrih, Prof. dr Ing. Dipl. Math Danilo P. Ra{kovi} redovni profesor Ma{inskihfakulteta u Beogradu, Ni{u i Kragujevcu, Mostaru i Filozofskog fakulteta u Novom Sadu, i wegov

doprinos razvoju nastave i studija Mehanike na Univerzitetima u Srbiji i Jugoslaviji, Round Table: O.M.History og Mecchanics in Yugoslavia, Proceedings on\f the YUCTAM Vrnja~ka Banjaa '97, XXII Yugoslav Congress ofTheoretical and Applid Mechanics, Mathematical Institute SANU, Jugoslovensko dru{tvo za mehaniku, 1997, str. 39-54.

11. Katica (Stevanovi}) Hedrih, Akademik Tatomir An|eli},@ivot i delo srpskih nau~nika - Lives and work of theSerbin Scientists, Urdenik Miloje R. Sari}, Biografije i Bibliografije, Kwiga VI, Odbor za prou~avawe`ivota i rada nau~nika u Srbiji i nau~nika srpskog porekla, Sarpska akdemija nauka i umetnosti, tom 6.,2000., str. 435-486.

Professor dr ing. Dipl. Math. Danilo P. Ra{kovi}, 90 years from the birth, by Katica (Stevanovi}) Hedrih, The FifthYugoslav Symposium on Nonlinear Mechanics, Nonlinear Sciences at the Threshold of the Third Millenium, October 2-5,2000, Ni{, Abstracts I, The Symposium is organised under the patronage of the Department of Technical Sciences SerbianAcademy of Sciences and Arts, 5th YUSNM Ni{ ' 2000, Faculty of Mechanical Engineering University of Ni{, pp. 84-85.

12. Professor dr ing. Dipl. Math. Danilo P. Ra{kovi}, 90 years from the birth, by Katica (Stevanovi}) Hedrih, The FifthYugoslav Symposium on Nonlinear Mechanics, Nonlinear Sciences at the Threshold of the Third Millenium, October 2-5,2000, Ni{, Abstracts II, Part D, Interdisciplinary and Multidisciplinary Problems, 5th YUSNM Ni{ ' 2000, Faculty ofMechanical Engineering University of Ni{, pp. 125-126.

13. Pola veka prirodno-matemati~kih nauka i 30 godina Prirodno-matematri~kog fakulteta u Novom Sadu, Novi Sad, 2000.14. Katica (Stevanovi) Hedrih, Close Meeting of the Threefold Kind at the Begining of Third Millenium or TensorCalculusBreak-impact in Mechanics, Invited Plenary Lecture, The 6-th International Conference of Tensor Society onDifferential Geometry and its Applications and Mathematical Foundations of Information Sciences and itsApplications on occasion of the Anniversary of Akitsugu KAWAGUCHIs 100 years birth, who is the Founder ofTensor Society, Kawaguchi Inst. Institute of Mathematical Sciences Sengen 1-13-33, Tsukuba, JAPAN, 305-0047.,Abstracts, Tensor Society, 2002., pp.8-10.

15. Simi, D.Profesor, dSp-mecatronic, Kragujevac, 1999. ID-78968588.

16. Katica (Stevanovi) Hedrih,Tensor Calculus Break-impact in Mechanics-Danilo P. Ra{kovi} (1910-1985),The SixthInternational Symposium on Nonlinear Mechanics-Nonlinearn Sciences and Applications, 2003., Booklet of

Abstracts,pp. 35-48.



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Prof. Dr. Ing. Dipl. Math. Danilo P. RAKOVI, full-professor

of the Faculties of Mechanical Engineering in Belgrade, Ni, Kragujevac, Mostar

and Faculties of Science in Belgrade and Novi Sad

On January 29th 1995 it was a two decade since our longtime professor and the first head of the

Department of Mechanics and Automatics within the Faculty of Mechanical Engineering of the University of Ni{,Prof. Dr. Ing. Dipl. Math. Danilo P. RAKOVI has died. He was a full-time professor of the faculties ofmechanical engineering in Belgrade, Ni, Kragujevac and Mostar, as well as of the faculties of science in Belgradeand Novi Sad.

This distinguished scientific figure of exquisite creative energy and inspired enthusiasm, a scholar deeplyattached to the Yugoslav and Serbian scientific and cultural heritage and an exquisite pedagogist of high ethicprinciples is in the living memory of many generations of students whom he taught how to learn and lovemechanics, as a basic scientific branch of mechanical engineering either directly, through his lectures, or throughhis various and numerous textbooks and collections of problems which circulate in more than 140,000 copies. Hisdisciples and colleagues are glad that he had the ability to transmit to them his great enthusiasm permeated with hissincere devotion for mechanics and his exquisite scientific eagerness.

Prof. Dr. Ing. Dipl. Math. Danilo P. RAKOVIwas born in 1910 in Uìce. Upon completing elementaryschool and six grades of high school, he graduated from the Military Academy in 1930. As an engineering military

officer he enrolled in the Department of Mechanical-Electrical Engineering of the Faculty of Engineering inBelgrade in 1933. Having graduated in 1938, he enrolled in the Department of Theoretical Mathematics of theFaculty of Philosophy and graduated in 1941. As a graduate mechanical engineer he was appointed assistant sectionhead of the Military-Technical Institute in â~ak. He remained on that position during 1941. In 1942 he wasappointed assistant of the Faculty of Engineering in Belgrade where he earned his doctor's degree in 1944 upon thedefense of the thesis entitled: "Tangential strains of normally profiled beams".

His university career took the following course: in June 1946 he was appointed assistant professor andlecturer; 1949 - associate professor; assistant professor of mechanics at the Faculty of Engineering; 1951 - associateprofessor; 1957 - full professor of mechanics.

Prof. Dr. Ing. Dipl. Math. Danilo P. RAKOVIlectured mechanics, strainght of materials and oscillationtheory at the faculties of mechanical engineering in Belgrade, Ni{, Kragujevac, Novi Sad and Mostar, as well as inthe Faculty of Science in Belgrade, Faculty of Philosophy in Novi Sad, Faculty of Electronics in Ni and at theMilitary-Technical College in Belgrade. More details on the research work of professor RAKOVIcan be found

in the Belgrade University Bulletin no. 75 of 1957, issued on the occasion of his appointment as full professor atthe Faculty of Mechanical Engineering in Belgrade. During his university career he was twice elected Vice-Dean ofthe Faculty of Mechanical Engineering of the Belgrade University. In the Mechanical Engineering Department ofthe Faculty of Engineering in Ni{, he lectured statistics, kinetics, kinematics, dynamics, oscillation theory,resistance of materials, theory of elasticity, as well as analytical mechanics, theory of nonlinear oscillations andcontinuum mechanics on the postgraduate level. He was the first head of Department of Mechanics and Automaticsof the Faculty of Mechanical Engineering in Ni{. He was an extremely inspired professor, scientist and practitionermuch favored among his students, respected by his colleagues both as a professor and an engineer, because heknew to relate engineering theory and practice.

Professor Ra{kovi} was a very fertile writer. While still in military service he wrote five professionalpapers. In the period before 1957, when he was appointed full professor, he published 26 scholarly papers. As a fullprofessor he wrote 37 scientific works published in the scientific journals of the Serbian Academy of Arts andSciences, Polish Academy of Science, German Society for Mechanics ZAMM and in other foreign journals. Hetook part in a number of scientific meetings in the country and abroad. He reviewed papers for four leading referraljournals in the world: Applied Mechanics Review (USA), Mathematical Reviews (USA), Zentrablatt (Germany)and Referativnii ùrnal (Moscow). Professor Ra{kovi} was a member of several professional and scientificsocieties/associations in the country and abroad, GAMM being one of them. He initiated the foundation of theYugoslav Society for Mechanics during 1952.

He wrote a considerable number of university textbooks which ran through numerous editions. Some ofthem still hold records as for the number of editions and copies printed within the group they belong to. In addition,he wrote a series of textbooks in the field of mechanics for secondary technical schools, as well as a number ofchapters in professional technical handbooks, mimeographed course materials and textbooks for post-secondaryschools of mechanical engineering. He also wrote several textbooks for postgraduate studies.



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We are of the opinion that this occasion should be used to say a few things about professor Ra{kovi}'sfour-year-long co-operation with the publishing house "Nau~na knjiga" concerning the publication of his universitytextbooks, collections of problems and various other handbooks. Follows the review of university textbooks andhandbooks written by professor Danilo Ra{kovi} and published by "Nau~na knjiga":

MECHANICS I (STATICS) - a 18,000-copy printing of first three editions; II edition 1949, III edition 1950; subsequent

editions 1960 (a 3,000-copy printing), 1962, 1964, 1965, 1968, 1971, 1973, 1978 (a 3,000-4,000-copy printing per edition)

MECHANICS II (KINEMATICS)- first two editions in a 13,000-copy printing. Editions: 1947, 1950, 1966.

MECHANICS III (DYNAMICS) - first two editions in 10,000 copies. Editions: 1947, 1956, 1962, 1973. COLLECTION OF PROBLEMS IN STRAINGHT OF MATERIALS - first two editions in a 6,000-copy printing.

Editions: 1947, 1955, 1965, 1967, 1971, 1975, 1981, 1985 - a 16,000-copy printing approximately.

STRAINGHT OF MATERIALS - editions: 1955, 1961, 1962, 1965, 1967, 1971, 1973, 1977, 1980, 1984 -

approximately 25,000 copies.

OSCILLATION THEORY- editions: 1957, 1965 - 6,000 copies.

TABLES OF STRAINGHT OF MATERIALS - (ran through 13 editions) approximately 40,000 copies.

ESSENTIAL MATRIX CALCULUS -1971 edition, 1,500 copies.

ELASTICITY THEORY - 1985 edition, 2,000 copies.

Some of his university textbooks were published by other publishing houses such as "Serbian Textbook PrintingOffice", "Gra|evinska knjiga", "Tehni~ka knjiga", among which the following ought to be mentioned: ESSENTIAL

THEORY OF MECHANISMS (1965) 2,000 copies; MECHANICS II (KINEMATICS), 1966 edition in 3,000 copies;

COLLECTION OF PROBLEMS IN MECHANICS III - OSCILLATION THEORY(1969) 2,000 copies.

Among professor Ra{kovi}'s textbooks for secondary technical schools the following deserve to be mentioned:

STATICS(a 9,000-copy printing), KINEMATICS(7,500), DYNAMICS(10,000).

Among the publications for postgraduate studies the following should be mentioned: ANALYTICAL MECHANICS

and TENSOR CALCULUS, both edited by the Faculty of Mechanical Engineering in Kragujevac.

Most of his university textbooks and publications were at the time of their first editions the only

professional literature in Serbian language in the field. So, his publications played an important part in spreadingthe knowledge in the field of technical mechanics among the students and mechanical and other engineers in Serbiaand Yugoslavia. It is particularly worth mentioning that he has interpreted all his material by the most modernmathematical apparatus and has illustrated it by numerous examples from the engineering practice. Many of thecited university publications are reprinted even now and are still used by both students of engineering and engineersthemselves.

Although he has left us ten years ago, professor Rakovi is still present among the new generations ofstudents, as well as among the engineers through his distinguished textbooks bearing memory of his merits whichhave left an indelible imprint on the development of mechanical engineering science and practice, as well as on theformation of many a generation of university professors. His life and work set an example serving as a creativeimpulse to the forth-coming generations educated at the University of Nis. He is an everlasting example and proofthat one's deeds can outlive one's physical existence by far.



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120.000 examples of university books in publishinghouse Nauna knjiga:

Author Prof. Dr. Ing. Dipl. Math. Danilo P. RAKOVI (1910-1985)

Hedrih (Stevanovi) R. KaticaMathematical Institute SANU Belgrade,

and Faulty of Mechanical Engineering University of Ni, Serbia

Abstract This distinguished scientific figure of exquisite creative energy and inspiredenthusiasm, a scholar deeply attached to the Yugoslav and Serbian scientific and culturalheritage and an exquisite pedagogist of high ethic principles is in the living memory ofmany generations of students whom he taught how to learn and love mechanics, as abasic scientific branch of mechanical engineering either directly, through his lectures, orthrough his various and numerous textbooks and collections of problems which circulatein more than 140,000 copies. His disciples and colleagues are glad that he had the abilityto transmit to them his great enthusiasm permeated with his sincere devotion formechanicsand his exquisite scientificeagerness.

Prof. Dr. Ing. Dipl. Math. Danilo P. RAKOVI lectured mechanics, strainght ofmaterials and oscillation theory at the faculties of mechanical engineering in Belgrade, Ni{,Kragujevac, Novi Sad and Mostar, as well as in the Faculty of Science in Belgrade,Faculty of Philosophy in Novi Sad, Faculty of Electronics in Ni and at the Military-Technical College in Belgrade.

Professor RAKOVIwrote a considerable number of university textbooks which ranthrough numerous editions. Some of them still hold records as for the number of editionsand copies printed within the group they belong to. In addition, he wrote a series oftextbooks in the field of mechanics for secondary technical schools, as well as a numberof chapters in professional technical handbooks, mimeographed course materials andtextbooks for post-secondary schools of mechanical engineering. He also wrote several

textbooks for postgraduate studies.We are of the opinion that this occasion should be used to say a few things about

professor Rakovi's four-year-long co-operation w ith the publishing house "Naunaknjiga" concerning the publication of his university textbooks, collections of problems andvarious other handbooks. Follows the review of university textbooks and handbookswritten by professor Danilo Rakovi and published by "Nauna knjiga" in total 120.000exemples:

* MECHANICS I (STATICS)- a 18,000-copy printing of first three editions; II edition 1949, III edition1950; subsequent editions 1960 (a 3,000-copy), 1962, 1964, 1965, 1968, 1971, 1973, 1978 (a 3,000-4,000-copy)

* MECHANICS II (KINEMATICS) - first two editions in a 13,000-copy printing. Editions: 1947, 1950,1966.

* MECHANICS III (DYNAMICS) -firsttwo editionsin 10,000copies.Editions:1947,1956,1962, 1973.* STRAINGHT OF MATERIALS- editions: 1955, 1961, 1962, 1965, 1967, 1971, 1973, 1977, 1980,

1984- approximately 25,000copies.* OSCILLATIONTHEORY - editions:1957, 1965- 6,000copies.* TABLES OF STRAINGHT OF MATERIALS - (ran through 13 editions) approximately 40,000copies.* ESSENTIAL MATRIX CALCULUS -1971 edition,1,500 copies.* ELASTICITY THEORY- 1985edition,2,000copies.

andother.Some of his university textbooks were published by other publishing houses such

as "Zavod za izdavanje udbenika", "Gradjevinska knjiga", "Tehnika knjiga".Among the publications for postgraduate studies the following should be mentioned:

ANALYTICAL MECHANICSand TENSOR CALCULUS, both edited by the Faculty ofMechanical Engineering in Kragujevac.All contents of these pubications are material resources existing as scientific

heritage in area of mechanics in Serbia and corresponding presentation in digital form isof great scientific interest and oppen possibilities to disseminate these foundamentalbooks in area on theoretical and applied mechanics to new generations of students,researchers and engineers.

ACKNOWLEDGEMENTS.

Sciences of Republic Serbiat ro ug h M at hem ati ca l Institute SANU BelgradeGrants ON144002 Th ti l d A li d

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