Mechanics Colloquim
PROGRAM
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:
Dragomir Zekovic, Masinski fakultet, Beograd
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.