Vol.6, No 1, 2007 pp.
65-73
UDC
531.5+534.24(045)=111
TWO REAL BODIES PROBLEM:
COMPLEX HARMONY OF MOTIONS
Milutin Marjanov
Faculty of Forestry, University of Belgrade
Abstract.
The gravitational interaction of two arbitrary shaped bodies, moving on the closed, periodic orbits is considered in this work. The stability of motions requires that every variable defining an aspect of the state has to be periodic and that any ratio between two arbitrary chosen periods of these variables has to be rational. It was shown in this work that such dynamical system implicates the perfect harmony of motions, with more than two hundred resonances.
Key words:
periodicity, resonances
PROBLEM DVA REALNA TELA:
SLOŽENA HARMONIJA KRETANJA
U radu se razmatra gravitaciona interakcija dva tela proizvoljnih oblika koja se kreću u zatvorenim, periodičnim orbitama. S obzirom da stabilna orbitalna i rotaciona kretanja zahtevaju da sve promenljive koje definišu stanje sistema moraju biti periodične i da se svaki par perioda mora stajati u odnosu celih brojeva, pokazano je da u posmatranom dinamičkom sistemu mora postojati preko dve stotine rezonanci.
Ključne reči:
periodičnost, rezonance
