National Institute of the Republic of Serbia
ὅδε οἶκος, ὦ ἑταῖρε, μνημεῖον ἐστιν ζωῶν τῶν σοφῶν ἀνδρῶν, καὶ τῶν ἔργων αὐτῶν
PROGRAM
PROGRAM ZA OKTOBAR 2013.
Pozivamo Vas da učestvujete u radu sednica Odeljenja i to:
Sreda, 9. oktobar 2013. u 18 casova, sala 301f:
Katica R. (Stevanovic) Hedrih, Matematicki institut SANU Beograd i Masinski fakultet Univerziteta u Nisu
DISCRETE FRACTIONAL ORDER SYSTEM DYNAMICS
Abstract: A theory of free vibrations of discrete fractional order system with finite number of degrees of freedom is founded in matrix form. Fractional order system wih finite number of degrees of freedom is defined by three matrices: matrix of mass inertia coefficients, matrix of system rigidity coefficients, matrix of the fractional order properties elements. By using matrix method a mathematical description of fractional order discrete system free vibrations is determined in form of coupled fractional order differential equataions. Corresponding solutions in analytical form for special case of the matrix of fractional order properties elements are determined in forms of polinomial series along time. For that case eigen characteristic numbers and corresponding system of eigen main coordinates as well as independent eigen fractional order modes are determined. Some graphical ilustrations of these eigen mail fractional order modes are presented on the basis of numerical data. A function of visoelastic creep fractional order dissipation of system energy and generalized forces of system with no ideal visoelastic creep fractional order dissipaion of system energy for generalized coordinates are introduced and deffined. Extended Lagrange differential equations second order for fractional order system dynamics in matrix formal form are introduced. A theorem is formulated. By use presented matrix method , as specal cases of the fractional order chain system are considered. Also, for a fractional order double DNA helix chain, the two coresponding main eiden chains as well as eigen modes are presented.
Sreda, 16. oktobar 2013. u 18 casova, sala 301f:
Dragomir Zekovic, Masinski fakultet, Univerzitet u Beogradu
DINAMIKA MEHANICKIH SISTEMA SA NELINEARNIM NEHOLONOMNIM VEZAMA - III ANALIZA KRETANjA (prvi deo)
Rezime. Analizira se kretanje neholonomnog mehanickog sistema sa dve materijalne tacke kojima se namece nelinearno ogranicenje na brzinama tih tacaka u vidu paralelnosti brzina. Za takav sistem se analiziraju: jednacine veza, reakcije veza, tj. nacin variranja takvih veza, trajektorije tacaka sistema, linearni integrali po generalisanim brzinama, tj. ciklicne koordinate. Na ovom modelu se jasno pokazuje da, u slucaju nelinearnih neholonomnih veza, Hamiltonovo dejstvo u opstem slucaju nema stacionarnu vrednost. Na kraju su izvedene jednacine brahistohronog kretanja opisanog sistema i odredjene brahistohrone pojedinih tacaka.
Sreda, 31. oktobar 2013. u 12 casova, sala 2, zgrada SANU, zajednicki sastanak sa Odeljenjem za matematiku Matematickog instituta SANU
Dzon Lenoks, Univerzitet u Oksfordu
Naslov i rezime predavanja bice naknadno objavljeni.
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.