The Second International Symposium on Nonlinear Dynamics
27-30 Oct.,2007, Shanghai, China, Ji-Huan He/ Chairman  
http://www.2007isnd.com/
http://www.2007isnd.com/

Proposal for minisymposa
the ANALYTICAL MECHANICS OF THE dyscrete HEREDITARY SYSTEMS
Chaiman
Katica (Stevanović) Hedrih
Faculty od Mechanical Engineering University of Niš, Mathematical Institute SANU,
Yu-18 000 - Niš,Ul.Vojvode Tankosica 3/22, Serbia
Telefax: 381 18 41 663  Mobile 063 8 75 75 99
e-mail: katica@masfak.ni.ac.yu - e-mail(houm): khedrih@eunet.yu

The investigation and construction  of Analytical Dynamics of Hereditary Discrete and Hybrid Systems play an important role in the study of rheolinear and nonlinear physical phenomena.
Recently only one monograph  and a series papers with some engineering applications were published in this special topic.
In current literature term “hereditary” and “rheological” systems are equivalent. In opinion of Работнов Ю.Н. [1], the name “hereditary” system or continuum proposed by В.Вольтерра, is more precise as well as suitable. By use this name, the property of rheological systems “to remember” history of loading is fully described. By series of the fundamental papers and monographs, Mechanics of hereditary continuum is presented. Also, in numerous references, many examples with applications in engineering, biological and other area [2] are published. Mechanics of discrete hereditary systems up to a few years before was presented only by separate single papers [3] and containing only solutions of the partial problems.
Research results in area of mechanics of the hereditary discrete systems, obtained by Oleg Aleksandrovich Goroshko and Katica (Stevanović) Hedrih, are generalized and presented in the monograph [4] which contains first presentation of the analytical dynamics of the hereditary discrete systems. We can conclude that this monograph contains complete foundation of the analytical dynamics theory of discrete hereditary systems and by using these results, numerous examples are obtained and solved (see Refs. [5-10]).
Keywords: hereditary system, rheological element, rheological and relaxational kernels, standard hereditary element, integro-differential equation, material particles, rheonomic coordinate, rheological coordinate, fractional order derivative,  rheological pendulum, rheonomic coordinate, covariant coordinate,thermo-rheological and piezo-rheological hereditary elements.

Basic references.

1. Работнов Ю.Н. Элементы наследственной механики твердых тел.–М.:Наука, 1977.–354 с.
2. Савин Г.Н., Рущицкий Я.Я. Элементы механики наследственных сред.–К.:Вища школа, 1975.-252 с.
3. Ржаницын А.Р. Некоторые вопросы механики систем, деформирующихся во времени.–М.:ГИТТЛ, 1949.–242 с.
4. Oleg Aleksandrovič Goroško (Ukrajina) iKatica (Stevanović) Hedrih (Serbia):Analitičkadinamika (mehanika) diskretnihnaslednihsistema, (AnalyticalDynamics (Mechanics) ofDiscreteHereditarySystems), UniversityofNiš, 2001, Monograph,  p. 426 (in Serbian), YU ISBN 86-7181-054-2.
5. Goroshko O.A. and Hedrih (Stevanović), K., (2007), Construction of the Lagrange mechanics of the hereditary systems, Minisymposium Oppening Lecture, Proceedings  of the International Summer School APM –Advanced Problem in Mechanics, Saint Petersburg 2007.(in press)
6. Hedrih (Stevanović), K., (2007), Energy analysis in the nonlinear hybrid system containing linear and nonlinear  subsystem coupled by hereditary element, Nonlinear Dynamics, Springer, DOI 10.1007/s11071-007-9197-2
7. Hedrih (Stevanović) K., (2006), Modes of the Homogeneous Chain Dynamics, Signal Processing, Elsevier,  86(2006), 2678-2702.. ISSN: 0165-1684  www.sciencedirect.com/science/journal/01651684
8. Hedrih (Stevanović) K., Rheonomic Coordinate method Applid to Nonlinear Vibration Systems with Hereditary Elements, Facta Universitatis, Series, Mechanics, Automatic Control and Robotics, Vol. 2, No. 10, 2000, pp. 1111-1135. YU ISSSN 0354-2009.
9. Hedrih (Stevanović) K., Thermorheological Hereditary Pendulum, (Ref. No. TVP-11) Thermal Stresses 99, Edited by J.J. Skrzypek and R. B. Hetnarski, Cracow 1999, pp.199-202.
10. Katica (Stevanović) Hedrih, Differential Equations of Two Mass Particles, Constrained with a Piezo-thermo-rheological Hereditary Element, Dynamics, Proceedings of full papers, Edited by Dragutin Veličković, 5 th International Conference on Applied Electromagnetics, PES 2001., pp. 77-80.

Prospective contributors are invited to submit their paper to Prof. Katica (Stevanović) Hedrih by email katica@masfak.ni.ac.yu or khedrih@eunet.yu All presented papers will be published in the Proceedings and the excellent papers will be recommended for publication in International Journal of Nonlinear Sciences and Numerical Simulations or Chaos Solitons and Fractals, or other journals after the Symposium.