Vol.1, No 7, 2000 pp. 911 - 923
UDC 531.3+621.83/85
STRUCTURAL STABILITY OF THE PLANETARY REDUCTOR NONLINEAR DYNAMICS PHASE PORTRAIT
Katica (Stevanović) Hedrih1, Rade Knežević2
1Faculty of Mechanical Emngineering University of Niš, Yugoslavia
2High Technical-Technology School in Vranje, Yugoslavia
e-mail: katica@masfak.masfak.ni.ac.yu
Abstract. Some results of numerical experiments on the planetary reductor nonlinear dynamics, and some properties in the nonlinear dynamics phase portrait in the area around singular saddle points and fixed points of the dynamical processes are presented in this paper.
This paper deals with the study of the configuration of the equilibrium positions of planetary reductors and their structural stability. The chosen reductor has its potential and kinetic energy as well as the modified form of the potential energy, by means of which the equilibrium positions are determined. The paper, also, gives the numerical experiment for the real planetary reductor, the dependence graphic between potential energy and the generalized coordinate and the dependence graphic between total energy of the system and the generalized coordinate. In addition, the paper presents the integral curves in the phase plane. The conclusion is drawn about the equilibrium positions and configurations under the dynamic conditions as well as about the equilibrium positions stability.
By using numerical experimental results on the planetary reductor nonlinear dynamics and phase portraits with total energy surfaces in phase space, we show that it is very important to know qualitative own properties of nonlinear dynamics change with small or slowchanging critical systems parameters to the structural stability of phase portrait.
Key words:  Nonlinear dynamics, planetary reductor, phase portrait, equilibrium positions, structural stability, numerical experiment, total energy surface, singular points, homoclinic trajectories
STRUKTURNA STABILNOST FAZNOG PORTRETA NELINEARNE DINAMIKE PLANETARNOG PRENOSNIKA
Rezultati numeričkog eksperimenta nad nelinearnim dinamikom planetarnog prenosnika su prikazani u ovom radu. Svojstva faznog portreta nelinearne dinamike planetarnog prenosnika u oblasti singularnih tačaka tipa sedla su izučavana i svetlu dinamičkih položaja ravnoteže sistema. Za studiranje strukturne stabilnosti faznog portreta nelinearne dinamike planetarnog prenosnika korišćena je analiza stacionarnih tačaka krivih potencijalne energije, ukupne energije sistema, kao i odgovarajuće grafičke prezentacije površi ukupne energije sistema, i njihove transformacije na promene parametara planetarnog prenosnika.
Iz analize su izvedeni zaključci o promeni kvalitativnih svojstva i osetljivosti strukturne stabilnosti faznog portreta na male promene nekih parametara sistema.
Ključne reči:  Nelinearna dinamika, planetarni reduktor, fazni portret, položaji ravnoteže, strukturna stabilnost, numerički eksperiment, površ ukupne energije sistema, singularne tačke, homokliničke trajektorije.