[institut] Plan rada za april 2015. godine

Fri Mar 27 10:23:06 CET 2015

Postovane kolege,

saljemo vam plan predavanja u okviru Odeljenja za mehaniku Matematickog
instituta SANU za april 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 APRIL 2015. GODINE

Sreda 1.4.2015. 18 casova, sala 301f
Katica R. (Stevanovic) Hedrih, Matematicki institut SANU

ELEMENTS OF GEOMETRY, KINEMATICS AND DYNAMICS OF BILLIARDS

'' In connection with the game of billiards .... there are various dynamic
tasks, whose solutions contain in this event.
I think that people who know Theoretical mechanics, and even students of
polytechnics, with interest familiarize themselves with explanations of all
the original phenomenon that can be observed from the time of movement
billiard balls”.

Gaspar-Gistav de Koriolis,

 Mathematical theory of billiards game.

G Coriolis (1990). Théorie mathématique des effets du jeu de billard ; suivi
des deux celebres memoires publiés en 1832 et 1835 dans le Journal de
l'École Polytechnique: Sur le principe des forces vives dans les mouvements
relatifs des machines & Sur les équations du mouvement relatif des systèmes
de corps (Originally published by Carilian-Goeury, 1835 ed.). Éditions
Jacques Gabay. ISBN 2-87647-081-0.

Abstract: Displays the elements of the dynamics of billiards, systems whose
dynamics are different phenomena observed dynamics of the system. Starting
from the geometric basis for switching to the impact theory, which is
basically a theory of the dynamics of each ball of billiards. Shown are the
plans of translational and angular velocities of rolling of one ball before
and after the collision, the two balls collide, as well as three balls in
simultaneous collisions. The equations are given for the impulse of movement
and kinetic energy before and after the collision in the aforementioned
cases.

Then expose the theory of the collision of two mass particles, as well as
two balls or impact of mass particle, as well as the balls in the barrier.
The output is hypotheses on collision and impact, define the various types
of collision and impact. This problem is associated with the dynamics of the
system with one side retaining constraints.

Will be talk about the competition and Royal Society. Royal Society Society
in London in 1668 announced a competition for the solution of problems of
the dynamics of impact and on this competition have submitted their works,
by now known scientists Vilis (Wallis, 1616-1703, Mechanica sive de
mote-1688) and Hajgens (Huygens – De motu corporum ex percusione). Using the
results of the collision submitted by the Royal Society learned Willis and
Huygens, and giving their generalizations, Isaac Newton founded the
fundamental basics of the theory of impacts. And before Newton and Huygens
and Willis, was exploring the dynamics of impacts. Thus, for example,
collision problems are dealt with Galileo Galilei, who came to the
conclusion that the impact force in relation to the pressure force
infinitely large, but it came to the knowledge of the relationship of impact
impulse and linear momentum.

It will be shown Karnoova teorema (Lazare Carnot 1753-1824., Principes
fondamenteaux de l’équilibre et de movement - 1803), who says that "In a
collision, the system inelastic material bodies loss of kinetic energy is
equal to the kinetic energy lost speed." The explanations on experimental
method for obtaining coefficients of restitution of different types of
impacts and collisions will be presented.

Comparing the elements of mathematical phenomenology and identifying
qualitative and mathematical analogy between geometry of moving geometric
point in the plane with defined constraints propagation ray of light with
the refusal of the obstacles and suggests that the trajectory of geometric
point and ray of light analogue and can be used as a baseline determination
of the trajectory of billiards ball.

But as billiard balls spherical bodies orbit of their dynamics depend on the
type of impact limiters in the form of the surface, and angles of impact
velocity and outgoing velocities of mass center balls depend on the type of
impact: whether the impact is skew or central! Only in the case that the
sphere neglected dimensions, so it can be regarded as a geometric point,
these angles are equal! In all other cases, the ball gets in the co
limitation kinetic energy of translation and rotation, a void to change the
angles of the outgoing and incoming velocity, if the balls are not
homogeneous and of equal mass.

The conclusion points to the importance of expanding elements of the
dynamics of billiards, crossing the dynamics discrete vibro-impacts systems,
particularly rolling heavy balls with mutual collisions, when the balls
rolling on curved lines that rotate. This dynamics is associated with the
dynamics of balls in rolling bearings.

Keywords: Billiards, ball, rolling without slipping, collision, alternation
of directional velocity, impact velocity, the uplink speed, trajectory of
the center of mass, central and skew collision, the impulse force, kinetic
energy, shock and collision, the collision of two balls, collision three
balls, rolling balls along rotate curvilinear lines, one side retaining
constraints.

Acknowledgment: Parts of this research were supported by Ministry of
Sciences of Republic Serbia trough Mathematical Institute SANU Belgrade
Grant ON174001:”Dynamics of hybrid systems with complex structures;
Mechanics of materials.”, and Faculty of Mechanical Engineering, University
of Niš.

References

1.        G Coriolis (1990). Théorie mathématique des effets du jeu de
billard ; suivi des deux celebres memoires publiés en 1832 et 1835 dans le
Journal de l'École Polytechnique: Sur le principe des forces vives dans les
mouvements relatifs des machines & Sur les équations du mouvement relatif
des systèmes de corps (Originally published by Carilian-Goeury, 1835 ed.).
Éditions Jacques Gabay. ISBN 2-87647-081-0. 

2.        G Coriolis (1832). "Sur le principe des forces vives dans les
mouvements relatifs des machines". J. De l'Ecole royale polytechnique 13:
268–302. 

3.        G-G Coriolis (1835). "Sur les équations du mouvement relatif des
systèmes de corps". J. De l'Ecole royale polytechnique 15: 144–154. 

4.        В.В. Коѕлов и Д. В. Тре¡в, Билиардì-Генетическое ббедение динамику
систем с ударами, Издателство Московского университета, 1991. Москва, стр.
192.

5.        Persson, A., 1998 How do we understand the Coriolis Force? Bull.
Amer. Meteor. Soc. 79, 1373-1385.

6.        Džamer, Maks (1957). Concepts of Force. Dover Publications, Inc..
ISBN 0-486-40689-X. 

7.        Robert Byrne (1990). Byrne's Advanced Technique in Pool and
Billiards. Harcourt Trade. p. 49. ISBN 0-15-614971-0.

8.       Hedrih (Stevanović) K., (2005), Nonlinear Dynamics of a Heavy
Material Particle Along Circle which Rotates and Optimal Control, Chaotic
Dynamics and Control of Systems and Processes in Mechanics (Eds: G. Rega,
and F. Vestroni), p. 37-45. IUTAM Book, in Series Solid Mechanics and Its
Applications, Editerd by G.M.L. Gladwell, Springer. 2005, XXVI, 504 p.,
Hardcover ISBN: 1-4020-3267-6.

9.       Hedrih (Stevanović) K., (2004), A Trigger of Coupled Singularities,
MECCANICA,  Vol.39, No. 3, 2004., pp. 295-314.  , DOI:
10.1023/B:MECC.0000022994.81090.5f,

10.    Hedrih (Stevanović), K., (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.

11.    Hedrih  (Stevanović K.,  (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.

12.    Hedrih  (Stevanović) K.,  (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.

13.    Hedrih (Stevanović) K., (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

14.    Hedrih (Stevanović) K R., Raičević V. and Jović 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.

15.    Hedrih  (Stevanović) K., Raičević V., Jović S., 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.

Sreda 8.4.2015. 18 casova, sala 301f
Dragoslav Sumarac, Gradjevinski fakultet Beograd

MODEL ZA ANALIZU OSTECENjA KONSTRKCIJA USLED CIKLICNIH PLASTICNIH
DEFORMACIJA

Rezime: Posmatra se najednostavniji nacin uvodjenja ostecenja konstrucija
koje nastaje kao posledica zamora u plasticnoj oblasti. Polazeci od
Prajzakovog histerezisnog opertaora, napravljen je model za analizu
elastoplasticnog ponasanja materijala pri aksijalnom naprezanju i savijanju
silama u plasticnoj oblasti. Usled plasticnih deformacija dolazi do pojave
zamornih prslina (ostecenja). U izlaganju ce biti pokazano da se i ovaj
fenomen moze modelirati uvodjenjem Prajzakovog operatora. Na nekoliko
primera resetkastih nosaca pokazane su prednosti ovog nacina modeliranja u
odnosu na postojece u literaturi i u komercijalnim programima (SAP, ABAQUS).

Sreda 22.4.2015. 18 casova, sala 301f
Bojan Arbutina, Matematicki fakultet, Univerzitet u Beogradu

EKSPLOZIVNI UDARI SA KOSMICKIM ZRACENjEM – MODIFIKOVANO SEDOVLjEVO RESENjE

Rezime: Udarni talasi javljaju se pri razmatranju raznih astrofizickih fenom
ena I objekata, poput supernovih i njihovih ostataka. Na ovom predavanju bic
e prikazano Sedovljevo resenje za eksplozivne udare,
koje opisuje evoluciju ostataka supernovih u adijabatskoj fazi. Razmotricemo
  i njegovu modifikaciju u slucaju prisustva kosmickog zracenja, odnosno, dod
atne komponente sa funkcijom raspodele cestica u faznom prostoru u obliku st
epenog zakona,
uz obican gas.

*******************

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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