[institut] Plan rada za septembar i oktobar 2015. godine (fwd)

Wed Sep 23 21:29:35 CEST 2015

Postovane kolege,

saljemo vam plan predavanja u okviru Odeljenja za mehaniku Matematickog
instituta SANU za septembar i oktobar 2015. godine.

Molimo vas da, ukoliko ste u
mogucnosti, prilozeni plan odstampate i okacite na oglasnim tablama vasih
institucija.

S postovanjem,
Katarina Kukic
Sekretar Odeljenja za mehaniku

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PLAN RADA ZA SEPTEMBAR I OKTOBAR 2015. GODINE

Sreda 30.9.2015. 18 casova, sala 301f

Srdjan Kostic, naucni saradnik, Institut za vodoprivredu ,,Jaroslav Cerni'',
Beograd
srdjan.kostic at jcerni.co.rs, srdjanrgf at gmail.com

NELINEARNA DINAMIKA SEIZMOGENIH RASEDA

Rezime: Seizmogeni rasedi predstavljaju mehanicke diskontiuitete u Zemljinoj
kori, po kojima kretanje u odredjenom velicinskom podrucju nije zanemarljivo
i moze da uslovi nastanak zemljotresa. Sa stanovista teorijske mehanike,
seizmicko kretanje duz raseda pokazuje svojstva stik-slip pomeranja, odnosno
aperiodicnog smenjivanja ciklusa naglog, kratkotrajnog kretanja velike
amplitude i dugotrajnog stacionarnog stanja (pomeranja vrlo male amplitude).
Sa stanovišta nelinearne dinamike, seizmicki rezim kretanja moze da se
objasni ili postojanjem stranog atraktora (deterministicki haos), ili
uticajem seizmickog suma. Na seminaru će biti prikazani rezultati
dosadasnjeg rada autora na izučavanju dinamike osnovnih mehanickih modela
pomeranja duz seizmogenih raseda. Modeli su predstavljani nizom blokova koji
su medjusobno povezani elasticnim oprugama i krecu se po hrapavoj povrsi.
Dinamika ovih modela definisana je sistemima diferencijalnih jednacina sa
kasnjenjem i sa sumom, pri čemu je kontakt blokova i hrapave povrsi određen
specificnim zakonima trenja zavisnim samo od brzine pomeranja blokova ili i
od brzine blokova i od stanja hrapavosti povrsi po joj se blokovi krecu.
Resenja ovih sistema jednacina, za odredjene vrednosti kontrolnih
parametara, ukazuju na pojavu bifurkacija u dinamickom sistemu, sa tipovima
oscilacija koji mogu odgovarati razlicitim rezimima seizmickog i aseizmickog
kretanja. Rezultati istrazivanja ukazuju na to da broj pokrenuti blokova u
funkciji njihove amplitude pokazuje karakteristicnu Gutenberg-Rihter
raspodelu, koja je utvrdjena da vazi za distribuciju realno osmatranih
zemljotresa.

Sreda 7.10.2015. 18 casova, sala 301f

Katica R. (Stevanovic) Hedrih, Matematicki institut SANU, Projekat ON174001

CENTRAL COLLISION OF TWO ROLLING BODIES: THEORY AND EXAMPLES OF VIBRO-IMPACT
SYSTEM NON-LINER DYNAMICS

Abstract: This chapter is focused to central collision of two rolling rigid
and heavy smooth balls and using elements of mathematical phenomenology and
phenomenological mapping obtain corresponding post collision and outgoing
angular velocities of the balls and applied these results for investigation
vibro-impact dynamics of two rolling balls along circle trace. This task is
fully solved and obtained results are original and new! Original plans of
component impact velocities and angular velocity of each of two different
rolling balls in central collision and corresponding outgoing angular
velocities are presented. Use Petroviċ’s elements of mathematical
phenomenology, especially mathematical analogy between kinetic parameters of
collision of two bodies in translator motion and collision of two rolling
different size balls, new original expressions of two outgoing angular
velocities for each of rolling balls after collision are defined. Using this
new and original result vibro-impact dynamics of two rolling different heavy
balls on the circle trace in vertical plane in period of series collisions
is investigated. Use series of the elliptic integrals, new nonlinear
equations for obtaining angles of balls positions at positions of collisions
are defined. Branches of phase trajectories of the balls in vibro-impact
dynamics are theoretically presented. Using previous new and original
result, the vibro-impact dynamics of two rolling heavy different disks on
the rotating circle trace in vertical plane in period of series of
collisions is investigated. Use series of the elliptic integrals, new
nonlinear equations for obtaining angles of disks positions at positions of
collisions are defined. Phase trajectories of the disks in vibro-impact
dynamics are theoretically presented. Two cases of vibro-impact dynamics
when phase portraits contain trigger of coupled singularities and homoclinic
orbit in the form of number “eight” as well as in the case without that
trigger of coupled singularities are discussed. Phase trajectory branches of
both rolling disks in period from initial positions to first collision
between rolling disks are presented.
Keywords: Theory, rolling balls, collision, pre-impact, post-impact,
impulse, moment of impulse, impact forces, impact couple, rolling trace,
arrival angular velocity, impact angular velocity, outgoing angular
velocity, theorems, collision of rolling balls in circle line, phase
trajectory, angular velocity discontinuity, collision of rolling disks on
rotate circle trace.

References
1. M. Petrovic, Elementi matematičke fenomenologije (Elements of
mathematical phenomenology), Srpska kraljevska akademija, Beograd, 1911.
str. 89.
http://elibrary.matf.bg.ac.rs/handle/123456789/476?locale-attribute=sr
2. M. Petrovic, Fenomenolosko preslikavanje (Phenomenological mapp), Srpska
kraljevska akademija, Beograd, 1933. str. 33.
http://elibrary.matf.bg.ac.rs/handle/123456789/475
3. Elements of mathematical phenomenology and phenomenological mapping in
non-linear dynamics, Edited by Katica R. (Stevanovic) Hedrih, Ivan Kosenko,
Pavel Krasilnikov and Pol D. Spanos, Special Issue of International Journal
of Non-Linear, Mechanics, Volume 73, Pages 1-128 (July 2015)
http://www.sciencedirect.com.proxy.kobson.nb.rs:2048/science/journal/002074
62/73
4. K. R. (Stevanovic) Hedrih, Beseda o Mihailu Petrovicu (Address to Mihailo
Petrovic) , Legende Beogradskog Univerziteta Legends about University of
Belgrade), Univerzitet u Beogradu, Univerzitetska biblioteka „Svetozar
Markovic“ u Beogradu, 2005, str. 37–-48.
5. K. R. (Stevanovic) Hedrih, Beseda o Mihailu Petroviću i fascinantnoj
nelinearnoj dinamici (Address about Mihailo Petrovic and fascinate
non-linear dynamics) , Rektorat Univerziteta u Beogradu i Srpska akademija
nauka i umetnosti, Maj mesec matematike –- Srpski matematicari , Naucni skup
maj 2012, Zavod za izdanje udzbenika, Beograd 2014-2015, pp. (to appear, in
press)
6. K. R. Hedrih (Stevanovic), V. Raicevic, S. Jovic, Vibro-impact of a Heavy
Mass Particle Moving along a Rough Circle with Two Impact Limiters, ©Freund
Publishing House Ltd., International Journal of Nonlinear Sciences &
Numerical Simulation 10(11): 1713-1726, 2009.
7. Hedrih (Stevanovic) K R., Raicevic V. and Jovic S., Phase Trajectory
Portrait of the Vibro-impact Forced Dynamics of Two Heavy Mass Particles
Motions along Rough Circle, Communications in Nonlinear Science and
Numerical Simulations, 2011 16 (12):4745-4755, DOI
10.1016/j.cnsns.2011.05.027.
8. K. R. Hedrih (Stevanovic) (200), Nonlinear Dynamics of a Gyro-rotor, and
Sensitive Dependence on initial Conditions of a Heav Gyro-rotor Forced
Vibration/Rotation Motion, Semi-Plenary Invited Lecture, Proceedings: COC
2000, Edited by F.L. Chernousko and A.I. Fradkov, IEEE, CSS, IUTAM, SPICS,
St. Petersburg, Inst. for Problems of Mech. Eng. of RAS, 2000., Vol. 2 of 3,
pp. 259-266.
9. K. R. Hedrih (Stevanovic) (2008), The optimal control in nonlinear
mechanical systems with trigger of the coupled singularities, in the book:
Advances in Mechanics : Dynamics and Control : Proceedings of the 14th
International Workshop on Dynamics and Control / [ed. by F.L. Chernousko,
G.V. Kostin, V.V. Saurin] : A.Yu. Ishlinsky Institute for Problems in
Mechanics RAS. – Moscow : Nauka, 2008. pp. 174-182, ISBN 978-5-02-036667-1.
10. K. R. Hedrih (Stevanovic) (2010), Discontinuity of kinetic parameter
properties in nonlinear dynamics of mechanical systems, Keynote Invited
Lecture, 9º Congresso Temático de Dinâmica, Controle e Aplicaçõesm, June
07-11, 2010. UneSP, Sao Paolo (Serra negra), Brazil, Proceedings of the 9th
Brazilian Conference on Dynamics Control and their Applications, Serra
Negra, 2010, pp. 8-40. SP - ISSN 2178-3667.
11. K. R. Hedrih (Stevanovic) (2012), Energy and Nonlinear Dynamics of
Hybrid Systems, Chapter in Book: Edited by A. Luo, Dynamical Systems and
Methods, Springer. 2012, Part 1, 29-83, DOI: 10.1007/978-1-4614-0454-5_2

Sreda 14.10.2015. 18 casova, sala 301f
Bozidar Jovanovic, Matematicki institut SANU

DINAMIKA BILIJARA I SIMETRICNE KVADRIKE

Rezime: Prikazacemo nove rezultate iz dinamike bilijara definisane
simetricnim kvadrikama u pseudo-Euklidskim prostorima. U slucaju kada su
trajektorije svetlosnog tipa, sistem se posmatra koristeci okvir kontaktne
integrabilnosti. Rad je motivisan istrazivanjima Vladimira Dragovica i
Milene Radnovic, a dobijen je u saradnji sa Vladimirom Jovanovicem
(Univerzitet u Banja Luci).

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Predavanja su namenjena sirokom krugu slusalaca, ukljucujuci studente
redovnih
i doktorskih studija. Odrzavaju se sredom sa pocetkom u 18 casova u sali
301f
na trecem spratu zgrade Matematickog instituta SANU, Knez Mihailova 36.

dr Katarina Kukic
Sekretar Odeljenja za mehaniku
Matematickog instituta SANU

dr Vladimir Dragovic
Upravnik Odeljenja za mehaniku
Matematickog instituta SANU

http://www.mi.sanu.ac.rs/colloquiums/mechcoll.htm
mehanika at mi.sanu.ac.rs

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