Vol.3, No 14, 2003 pp. 865-879
UDC 531+532+534+517.93
Invited Paper
NONLINEAR PHENOMENA IN DYNAMICS OF CAR MODEL
Katica (Stevanović) Hedrih, Julijana Simonović
Faculty of Mechanical Engineering University of Niš
Mathematical Institute SANU Belgrade
Yu-18 000- Niš, ul. Vojvode Tankosi?a 3/22,
Telefax: 381 18 41 663, Mobile 063 8 75 75 99
e-mail: katica@masfak.ni.ac.yu * khedrih@eunet.yu * sjupe@ptt.yu
Abstract. In this paper research results of influences, of masses debalances of car system and of rough spot (prominence) in the way on which the car is in move, at nonlinear dynamics properties of car are presented. Also, the properties of nonlinear dynamics of car model are investigated by using the corresponding equations of phase trajectories of corresponding basic scleronomic nonlinear model to the rheonomic car dynamics model. Particularly we were analyzed homoclinic orbits and their transformation shaped by number eight, there appear and disappear are caused by changing some parameters of system. By using Math-Cad program for drawing families of phase portraits visualization of nonlinear phenomena in dynamic of car model are presented, also on that graphics it is barely noticeable a influence of masses debalances parameters like as of rough spot (prominence) in the way at nonlinear dynamics features of car.
It is observe one system of tree degree of mobilities and with one degree of freedom and we narrow our problem on research of  following nonlinear differential equation:

like as homogenous equation appropriate to this equation:

From characteristics visualizations we can noticeable the phenomena of trigger of coupled singularities and homoclinic orbits shaped by number eight like as double number eight. Analyzing the properties of basic nonlinear system we comes to conclusion that with modification of parameters of system appears a separation of one homoclinic orbits in more, like as that becomes to bifurcation of relative rest position in rheonomic system, apropos in equivalent scleronomic system which correspond to him.
Key words:  Car model, rough spot (prominence) in the way, nonlinear dynamics, phase portrait, trigger of coupled singularities, homoclinic orbit,
layering of homoclinic orbit.

NELINEARNI FENOMENI U DINAMICI MODELA VOZILA
U radu su predstavljeni rezultati proučenih uticaja debalansa masa vozila i neravnine puta po kojoj se posmatrano vozilo kreće na osobenosti njegove nelinearne dinamike. Izvedene su jednačine faznih trajektorija relativne dinamike i proučena svojstva i struktura faznih portreta nelinearne dinamike baznpg scleronomnog modela koji odgovara reonomnom modelu takvog modela vozila. Posebno su analizirani oblici homokliničkih orbita i transformacija homokliničkih orbita oblika broja osam, čije postojanje i nepostojanje je vezano za odredjenu promenu parametara sistema. Pomoću MathCad programa sastavljene su familije faznih portreta baznog sistema, i faznih trajektorija izučavanog sistema, tako da je pomocu njih data vizuelizacija nelinearnih fenomena u dinamici modela vozila i slikovito je prikazan uticaj parametara debalansa rotacionih masa, kao i neravnine puta na svojstva nelinearne dinamike modela vozila.
Posmatran je sistem sa tri stepeni pokretljivosti i jednim stepenom slobode kretanja i zadatak se sveo na izučavanje sledeće nelinearne diferencijalne jednačine

kao i njoj odgovorajuće homogene oblika:

Sa karakterističnih vizualizacija dinamike baznog sistema uočava se pojava trigera spregnutih singulariteta i homokliničkih orbita u obliku broja osam, kao i udvojenih brojeva osam. Analizom svojstava osnovnog nelinearnog sistema dolazi se do zaključka da se sa promenom parametara sistema javlja raslojavanje jedne homokliničke orbite u više, kao i da dolazi do bifurkacije položaja relativnog mirovanja u reonomnom sistemu, odnosno položaja ravnoteže u ekvivalentnom skleronomnom sistemu koji mu odgovara. U tome se objašnjava pojava sličnih haotičnim i stohastičnim kao odziv na sasvim periodične pobude.