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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 OKTOBAR 2014.

Pozivamo Vas da učestvujete u radu sednica Odeljenja i to:

Sreda, 8. oktobar 2014. u 18 casova, sala 301f:
Katica R. (Stevanovic) Hedrih , Mathematical Institute SANU Belgrade, Department for Mechanics and Faculty of Mechanical Engineering, University of Nis, Serbia.
ENERGY DISSIPATION IN DYNAMICS OF A CLASS OF THE FRACTIONAL ORDER SYSTEM

Abstract. Starting from matrix fractional order differential equation of a class of the system dynamic with finite number of degrees of freedom, and fractional order energy dissipation, relation between total mechanical energy (sum of kinetic and potential energies) and generalized function of fractional order energy dissipation is derived. Also using formulas of transformation from system independent generalized coordinates and eigen main coordinates of considered class of fractional order system dynamics relation between total mechanical energy (sum of kinetic and potential energies) and generalized function of fractional order energy dissipation on one eigen main fractional order mode is derived. On the basis of these relations, two theorems of energy fractional order dissipation of a class of the fractional order system with finite number of degrees of system, are defined and proofed.

Keywords: Fractional order system, generalized function of fractional order energy dissipation, theorem of mechanical energy change, qualitative and mathematical analogies, eigen main fractional order mode energy dissipation.

References

[1] O.A. Gorosko and K.R. Hedrih (Stevanovic), (2001), Analiticka dinamika (mehanika) diskretnih naslednih sistema, (Analytical Dynamics (Mechanics) of Discrete Hereditary Systems), University of Nis, 2001, Monograph, p. 426, YU ISBN 86-7181-054-2.

[2] O.A. Gorosko and K.R. Hedrih (Stevanovic), The construction of the Lagrange Mechanics of the discrete hereditary systems, FACTA UNIVERSITATIS, Series: Mechanics, Automatic Control and Roboticsod Vol. 6, No 1, 2007, pp. 1 __- 22.

[3] K.R. Hedrih (Stevanovic), The Dissipation Function of a Nonconservative System of Mass Particles, Tensor, N.S.,Vol.63, No.2(2002), pp.176-186. Tensor Society , Japan .

[4] K.S. Hedtrih (Stevanovic) K., (2011), Analytical mechanics of fractional order discrete system vibrations. Chap in Monograph. Advances in nonlinear sciences, V.l. 3, JANN, Belgrade, pp. 101-148, 2011. ISSN: 978-86-905633-3-3.

[5] K.R. Hedtrih (Stevanovic), (2008), The fractional order hybrid system vibrations, Monograph, Chap in Monograph. Advances in Nonlinear Sciences, ANN, 2008, Vol. 2, pp. 226-326.

[6] K.R. Hedrih (Stevanovic), (2004), Discrete Continuum Method, COMPUTATIONAL MECHANICS, WCCM VI in conjunction with APCOM.04, Sept. 5-10, 2004, Beijing, China, 2004 Tsinghua University Press & Springer-Verlag, pp. 1-11, CD. IACAM International Association for Computational Mechanics . www. iacm.info

[7] K.R. Hedtrih (Stevanovic), (2009), Considering Transfer of Signals through Hybrid Fractional Order Homogeneous Structure, Keynote Lecture, AAS-09, Ohird, Makedonija, posvecen profesoru Pane Vidincevu, prvom profesoru automatike i rachnarskih mashina u Makedoniji Special session, Applied Automatic Systems , Proceedings of selected AAS 2009 Papers. Edited by G. Dimirovski, Skopje .Istambul , 2009, ISBN -13-978-9989-2175-6-2, National Library of R. Makedonia, Skopje, Copright2009Authors and ETAI Society, pp. 19-24.

[8] A. N. Hedrih, K.R. Hedrih(Stevanovvic), (2013), Modeling Double DNA Helix Main Chains of the Free and Forced Fractional Order Vibrations, Chapter in Book Advanced topics on fractional calculus on control problem, modeling, system stability and modeling, Editor M. Lazarevic, (2013), pp. 145-183 and Appendix pp. 192-200. . WORLD SCIENTIFIC PUBLISHING COMPANY PTE LTD

[9] K. R. Hedrih (Stevanovic), (2013), Fractional order hybrid system dynamics, PAMM, Proc. Appl. Math. Mech. 13, 25 . 26 (2013) / DOI 10.1002/pamm.201310008

http://onlinelibrary.wiley.com/doi/10.1002/pamm.v13.1/issuetoc

[10] K. R. Hedrih (Stevanovic), (2013), Generalized function of fractional order dissipation of system energy and extended Lagrange differential equation in matrix form, Dedicated to 86th Anniversary of Radu MIRON.S Birth. 30 minutes, Plenary Lecture, Abstracts of THE 13th INTERNATIONAL CONFERENCE OF TENSOR SOCIETY ON DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, AND INFORMATICS BESIDES., The 86th Anniversary of Radu MIRON.S Birth. September 3rd (Tuesday) to September 7th (Saturday) in 2013. Faculty of Mathematics, Alexandru Ioan Cuza University and Mathematical Institute .O.Mayer. in Ia.i Romania And Tensor Society, Japan, 2013, p.3. (paper submitted for publishing in the journal Tensor of Tensor Society, Japan.)

http://www.math.uaic.ro/~tensorconference2013/

[11] K. R. Hedrih (Stevanovic), A. N. Hedrih, Phenomenological mapping and dynamical absorptions in chain systems with multiple degrees of freedom, Journal of Vibration and Control 1077546314525984, first published on March 19, 2014 as doi:10.1177/1077546314525984

Sreda, 22. oktobar 2014. u 18 casova, sala 301f:
DINAMIKA MEHANICKIH SISTEMA SA NELINEARNIM NEHOLONOMNIM VEZAMA - III ANALIZA KRETANJA , Treci deo

Rezime. Analizira se kretanje neholonomnog sistema od dve tacke kojima je nametnuto nelinearno ogranicenje u vidu upravnosti brzina. Za takav sistem se vrsi analiza: jednacine veze, reakcije veze tj. nacin variranja te veze, linearnih integrala po generalisanim brzinama tj. ciklicnih koordinata, stacionarnosti Hamiltonovog dejstva, jednacina brahistohronog kretanja i trajektorija tacaka sistema.

Sreda, 29. oktobar 2014. u 18 casova, sala 301f:
Bozidar Jovanovic, Matematicki institut SANU
NEHOLONOMNA DINAMIKA U R^n

Rezime. Razmotricemo razne neholonomne modele kretanja visedimenzionog krutog tela. Posebno cemo analizirati kotrljanje bez klizanja balansirane, dinamicki nesimetricne lopte u R^n.

Reference

[1] Fedorov Yu N, Kozlov V V, Various aspects of \$n\$-dimensional rigid body dynamics, Amer. Math. Soc. Transl. Series 2, 168 (1995) 141-171.

[2] Jovanovic B, Hamiltonization and Integrability of the Chaplygin Sphere in R^n, J. Nonlinear Sci. 20 (2010) 569-593.

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