BEGIN:VCALENDAR VERSION:2.0 PRODID:-//CERN//INDICO//EN BEGIN:VEVENT SUMMARY:Dynamics of Gyro-rotors: Theory and Applications DTSTART;VALUE=DATE-TIME:20101222T170000Z DTEND;VALUE=DATE-TIME:20101222T180000Z DTSTAMP;VALUE=DATE-TIME:20261010T103353Z UID:indico-event-40@indico.ipb.ac.rs DESCRIPTION:Brief review of realized models of gyro-rotors\, applied gyr c ontrol and stabilizations and motion of ships\, aircrafts\, vehicles\, and torpedo. With development of micro and nano- technology it feels a need f or new class of gyroscopic systems. An analysis of principle of gyro-syste m work is presented as well as analysis of component motions. Most of real ized gyro-stabilizators are realized on the basis of coupled rotations\, w ith resultant rotation around fixed point. Gyroscopic moments are analyzed . (see References [1-2]\, [9-10]\, [15-16]). For a model of gyro-rotor\, b y use vector method\, based on the mass moment vectors for an axis and pol e\, introduced by Hedrih (Stevanovic) K. [4-8]\,\, vector expressions for linear momentum and angular momentum of a heavy rigid body rotation around two axes without intersection are derived\, as well as their derivatives. These vector expressions are used for obtaining expressions of the kineti c parameters of nonlinear dynamics of considered system dynamics or vibrat ions. The following vector expressions: for kinetic pressures to bearings on the self rotation axis and to the axis of precession rotation\, as well as their components are pointed out and analyzed. For the special case th at heavy rigid disk is eccentrically and skew positioned on the self rotat ion axis which rotate in the horizontal plane around vertical axis with co nstant angular velocity on a distance\, we derived: the nonlinear differen tial equation of the system dynamics in the gravitational field and corres ponding equations of the phase trajectory as well as kinetic pressure comp onents on self rotation bearing and vector rotator. Series of graphical pr esentation are presented.- - - - - - - - - -Daje se pregled realizovanih m odela girorotota koji su u upotrebi i koji se koriste za upravljanje i sta bilizaciju kretanja brodova\, aviona\, vozila\, letilica\, i torpeda. Sa r azvojem mikro i nano tehnologija javila se potreba za novom klasom girosko pa pa se najavljuju novi modali\, kao i savremenim pravcima razvoja. Daje se analiza principa rada i vrsta kretanja. Analiziraju se odgovarajuće ki nematičkih i kinetičkih paarametara dinamike postojećih izvedenih model a girostabiliz i ukazani na vrste kretanja. Većina starih uređaja je izv edena na bazi složenih spregnutih komponentnih rotac koje rezultiraju u o brtanje girost oko nepomične tačke. Ukazuje se i na izvore giroskopskih momenata kojima se vrši stabilizacija ili upravljanje kretanja. Na primer u jednog girorotora prikaѕuju se neki kinetički parametri girorotora i u kazuje se na pojavu novih modela namenjenih mikrouređajima. (Reference [1 -2]\, [9-10]\, [15-16]).Za izabrani model girorotota\, koji se sastoji od teškog krutog tela\, koje se obrće oko dve mimoilazne ose\, vektorkom me todom\, zasnovanom na korišćenju vektora momenata masa vezanih za pol i osu\, koje je uvela K. Hedrih [4-8]\, izvedeni su vektorski izrazi za koli činu kretanja i moment količine kretanja\, kao i odgovarajući izvodi po vremenu. Telo je ekscentripno postavljeno u odnosu na osu sopstvene rotac ije\, a ni jedna glavna centrana osa inercije teškog krutog tela nije par alelna sa osom sopsvene rotacije tela\, sto znači da je teko koso postavl jeno u odnosu na istu. Za tako definisani maretijalni sistem u polju zemlj ine teže\, kada je kruto telo disk ekscentrično i koso postavljen i za s lučaj da je osa sopstvene rotacije u horizontalnoj ravni\, a osa prenosno g kretanja vertikalna i da je ugaona brѕzina prenosnog kretanja konstantn a\, a ose mimoilazne izvedeni su: nelinearna diferencijalna jednačina sop stvene rotacije\, jednačina faznih trajektorija\, izrazi za kinetičke pr itiske u vektorskom obliku\, kao i odgovarajući vektori rotatori i ugaone brzine njihove ritacije oko ose sopstvene rotacije. Dara je analiza svojs tava komponenata kinetičkih pritisaka na režišta ose sopstvene rotacije . Korišćenjem MathCad Software sastavljene su serije grafičkih prikaza: faznih portreta\, intenzteta vektora rotatora i njegove ugaone brzine obt anja oko sopstvene ose rotacije girorotota\, intenziteta komponenata kinet ičkih pritisaka u zavisnosti od ekcentriciteta diska i ugla njegovog nagi ba u odnosu na osu sopstvene rotacije\, kao i rastojanja mimoilaznih osa p renosnog i sopstvenog obrtanja. Pokazuju se neka svojstva i identifikuju f iksne tače na tim dijagramima kada se menjaju parametri ekscentričnosti\ , ugla nagiba diska ili rastojanja između mimoilaznih osa (Reference).Ref erences[1]  Avramov K.\, Borysluk O.\, Bifurication of Elastic Rotors in Journal Bearings\, The Third  International Conference Nonlinear Dynamics – 2010\, pp. 21-26[2]  Bulьakov B. V.\, Prikladnaя teoriя giroskopo v\, Izdatelstvo Moskovskogo universiteta\, 1976\, 400[3] S.K. Kim\, D. M. Tilbury: Mathematical Modeling and Experimental Identification of a Model Helicopter\, in Journal of Guidance\, Control and Dynamics\, August 31\, 2 000[4]  Hedrih (Stevanović)\, K.\, The Vector Method of the Heavy Rotor Kinetic Parameter Analysis and  Nonlinear Dynamics \, Monograph\,  Unive rsity of Niš\, 2001\, pp. 252.\, YU ISBN 86-7181-046-1.[5]  Hedrih (Stev anović)\, K.\, (1992)\, On some interpretations of the rigid bodies kinet ic parameters\, XVIIIth ICTAM HAIFA\, Apstracts\, pp. 73-74. [6]  Hedrih (Stevanović)\, K. (1998)\, Vectors of the Body  Mass Moments\, Monograph paper\, Topics from Mathematics and Mechanics\, Mathematical institute SA NU\, Belgrade\, Zbornik radova 8(16)\, 1998\, pp. 45-104.  published in 1 999. (in English)\, (Zentralblatt Review).[7]  Hedrih (Stevanović)\, K.\ , (1993)\,  Same vectorial interpretations of the kinetic parameters of s olid material lines\, ZAMM. Angew.Math. Mech. 73(1993) 4-5\, T153-T156.[8]   Hedrih (Stevanović)\, K.: (1993)\, The mass moment vectors at n-dimens ional coordinate system\, Tensor\, Japan\, Vol 54 (1993)\, pp. 83-87.[9]  S.K. Kim\, D. M. Tilbury: Mathematical Modeling and Experimental Identifi cation of an Unmanned Helicopter Robot with Flybar Dynamics\, in  Journal of Robotic Systems 21 (3)\, 95-116 (2004)\, 2004 Wiley Periodicals\, Inc. Published online in Wiley Inter Science (www.interscience.wiley.com)\, DO I: 10. 1002/rob.20002[10] Stephen C. Spry\, Anouck R. Girard: (2008)\, Gyr oscopic Stabilization of Unstable Vehicles: configurations\, dynamics and control\, in Vehicle System Dynamics\, Volume 46\, Issue S1 2008\, pp.247- 260\, DOI: 10.1080/00423110801935863[11]   Katica (Stevanović) Hedrih  and Ljiljana Veljović\, (2008)\, Nonlinear dynamics of the heavy gyro-ro tor with two skew rotating axes\, Journal of Physics: Conference Series\, 96 (2008) 012221 DOI:10.1088/1742-6596/96/1/012221\, IOP Publishing http:/ /www.iop.org/EJ/main/-list=current/[12]  Hedrih (Stevanović) K.\, A Trig ger of Coupled Singularities\, MECCANICA\,  Vol.38\, No. 6\, 2003.\, pp. 623-642.  \, International Journal of the Italian Association of Theoreti cal and Applied Mechanics\, CODEN MECC B9\, ISSN 025-6455\, Kluwer Academi c Publishers[13]  Hedrih (Stevanović K.\, (2008)\, The optimal control i n nonlinear mechanical systems with trigger of the coupled singularities\, in the book: Advances in Mechanics: Dynamics and Control: Proceedings of the 14th International Workshop on Dynamics and Control / [ed. by F.L. Che rnousko\, G.V. Kostin\, V.V. Saurin] : A.Yu. Ishlinsky Institute for Probl ems in Mechanics RAS. – Moscow: Nauka\, pp. 174-182\, ISBN 978-5-02-0366 67-1.[14]  Hedrih (Stevanović) K\, Veljović Lj.\, (2010)\, The Kinetic Pressure of the Gzrorotor Eigen Shaft Bearings and Rotators\, The Third  International Conference Nonlinear Dynamics – 2010\, pp. 78-83[15]  Yu. G. Martynenko\, I. V. Merkuryev\, V. V. Podalkov: Control of Nonlinear Vi brations of Vibrating Ring Micro gyroscope\, in Mechanic of Solids\, 2008\ , Vol. 43\, No. 3\, pp. 379-390\, Allerton Press\, Inc.\, 2008\, ISSN 0025 -6544[16]  Strogatz\, Steven H. (1994). Nonlinear Systems and Chaos\, Per seus publishing \n\nhttps://events.saifa.rs/event/40/ LOCATION:Mathematical Institute 301 F URL:https://events.saifa.rs/event/40/ END:VEVENT END:VCALENDAR