Stability of the relative equilibria in the generalized J2 problem

• Published in: Serbian astronomical journal. Vol. 2000; no. 161; pp. 9 - 13
• Main Authors: Mioc, V., Stavinschi, M.
• Format: Journal Article
• Language: English
• Published: Astronomical Observatory, Department of Astronomy, Belgrade 2000
• ISSN: 1450-698X; 1820-9289
• DOI: 10.2298/SAJ0061009M

For a large class of concrete astronomical situations, the motion of celestial bodies is modelled by dynamical systems associated to a potential function ?/r + ?U (r = distance between particles, ? = real constant, ? = real small parameter, U = perturbing potential). In this paper the nonlinear stability of the relative equilibrium orbits corresponding to such a potential is being investigated using a less usual method, which combines a block diagonalization technique with the reduction procedure. The test points out certain nonlinearly stable orbits, and is inconclusive for the remaining equilibria. The latter ones are treated via linearization; all of them prove instability. The nonlinearly stable orbits remain stable under any perturbation that preserves the conserved momentum. Za jednu veliku klasu konkretnih astronomskih situacija modelirano je kretanje nebeskih tela u dinamickim sistemima za koje vazi potencijalna funkcija ?/r + ?U (r = rastojanje izmedju cestica, ? = realna konstanta, ? = realni mali parametar, U = poremecajni potencijal). U ovom se radu istrazuje nelinearna stabilnost relativno uravnotezenih orbita koje odgovaraju takvom potencijalu koristeci jednu manje uobicajenu metodu a koja spaja tehniku blok dijagonalizacije i postupak svodjenja. Test istice izvesne nelinearno stabilne orbite dok je neodredjen za ostale ravnoteze. Nelinearno stabilne orbite ostaju stabilne pri svakom poremecaju koji zadrzava konzervisani momenat.