﻿ MISANU
ὅδε οἶκος, ὦ ἑταῖρε, μνημεῖον ἐστιν ζῴων τῶν σοφῶν ἀνδρῶν, καὶ τῶν ἔργων αὐτῶν

Mechanics Colloquim

PROGRAM

MATEMATIČKI INSTITUT SANU
ODELJENJE ZA MEHANIKU

PROGRAM ZA NOVEMBAR 2005.

Pozivamo Vas da učestvujete u radu sednica Odeljenja i to:

SREDA, 02. novembar 2005. u 18 sati:

Ilustracija pocetka vasione II

Prikazuju se dva primera polja ciste radijacije kao ilustracija Hokingovog odgovora na pitanje sta je bilo pre pocetka sirenja vasione (po teoriji velikog praska).

SREDA, 09. novembar 2005. u 18 sati:

Livija Cveticanin
KRETANJE TELA SA PREKIDNOM PROMENOM MASE

Analizira se kretanje krutog tela mase M od kojeg se odvoji telo mase m. Posmatraju se tri intervala kretanja: a) kretanje celog tela, b) razdvajanje tela na dva dela, i najzad, c) kretanje preostalog dela tela. Centralno mesto u istraivanjima vezano je za samo razdvajanje tela. Uvodei odredjene pretpostavke i ogranienja i primenjujui osnovne zakone mehanike i teoriju udara analiziran je proces razdvajanja tela. Kao specijalan sluaj proueno je ravansko kretanje tela u sve tri etape kretanja. Teoretska razmatranja i rezultati primenjeni su na analizu kretanja rotora od kojeg se odvoji deo. Odredjeni su uslovi asimptotski stabilnog kretanja preostalog dela rotora nakon odvajanja dela rotora.

SREDA, 16. novembar 2005. u 18 sati:

Mihailo.P.Lazarevic
Further results on applications of fractional calculus in mechanics and control theory

This presentation is aimed at the engineering and/or scientific professional who wishes to learn about fractional calculus and its possible applications in their fields of study.The intent is to first expose the listener to the concepts, definitons, and execution of fractional calculus and second to show how these may be used to solve several modern problems. First of them is examle of a new theory of electroviscoelasticity which describes the behavior of electrified liquid-liquid interfaces in fine dispersed systems, and is based on a new constitutive model of liquids: fractional order model (generalized the Van der Pol equation) with corresponding fractional-order time derivative and integral of order < 1, especially linear and nonlinear case. Also, in this presentation stability test procedure is shown for (non)linear (non) homogeneous time-invariant fractional order systems (LTI FOS). Here, some basic results from the area of finite time and practical stability extends to (non)linear, continuous, fractional order time invariant time-delay systems given in state space form. Sufficient conditions of this kind of stability, for this particular class of fractional time-delay systems are derived.Specially, previous results can be applied for robotic system where it appears a time delay in fractional control system.At last, a new algorithm for iterative learning control (ILC) is proposed for fractional linear time delay system, where using fractional-order derivative of tracking error one can obtain a type ILC. Sufficient conditions for the convergence of a proposed type of learning control algorithm for a class of fractional state space LTI system with time delay are also presented.

SREDA, 23. novembar 2005. u 18 sati:

Jovo Jaric, Dragoslav Kuzmanovic, Zoran Golubovic
On the State of Pure Shear
It is known that in classical continuum mechanics the Cauchy stress tensor T is symmetric. By definition, a state of stress is said to be one of pure shear if there is an orthogonal basis p_i (i = 1; 2; 3) for which p_i * Tp_i = 0; (no sum over indices i = 1; 2; 3) Theorem 1 A necessary and suficient condition for T to be a state of pure shear is trT = 0.
Recently, Belik and Fosdick [1], in order exhibits all such bases, gave complete discussion of this fundamental theorem from both the geometric and algebraic points of view. Very recently, Boulanger and Hayes [2] presented what they called "an even more elementary proof and give an insightful geometrical approach". They also that "it may be shown that n*Tn = 0 for all n lying in a plane, if and only if one of eigenvalue is zero, and all the n lie in either one or other of the planes of central circular section of ellipsoid E, the planes with normals h_{+,-}". But, in order to proof the theorem we do not need any ellipsoid. More over, here we present the proof making use only of the notion of orthogonal projector. The proof includes also the above case.

References [1] P. Belik and R. Fosdick, The state of pure shear, Journal of Elasticity, 52, 91-98, 1998.
[2] Ph. Boulanger and M. Hayes, On Pure Shear, Journal of Elasticity, 77, 83-89, 2004.

SREDA, 30. novembar 2005. u 18 sati:

Veljko Vujicic
Princip dejstva sile

Sadraj: Saoptenja u Seminaru reologije za vreme bombardovanja 1999, na Medjunarodnom kongresu u Moskvi 2002. i na Jugoslovenskom kongresu u Novom Sadu 2005. Oponentski stavovi. Treci Njutnov aksiom ili zakon akcije i reakcije. Pojam principa mehanike, dejstva sile, virtuelnog pomeranja. Definicija pojma protivdejstvo sile. Princip protivdejstva sile.

Sednice se održavaju u zgradi SANU, Knez Mihailova 35, u sali 2 na prvom spratu.

Sekretar Odeljenja
dr Božidar Jovanović
Upravnik Odeljenja