The restricted gravitational three-body problem trajectories associated with Lagrange fixed points

Abstract

Studies of the restricted three-body problem can help in understanding the dynamics of three-body interactions in the solar system. In the rotating coordinate system based on the two principal bodies there are five fixed Lagrange points. The equations of motion of the third body near a Lagrange point may be linearized, showing that under certain conditions there can be librational motion about the Lagrange points. Some examples of numerical studies of trajectories associated with Lagrange points are shown in inertial and in rotating coordinates, and are discussed. The examples include librations, horseshoe orbits and chaotic orbits. The restricted three-body problem, with its four degrees of freedom, provides considerable opportunities for project work in computational physics.} (Serbian). Rad na analizi problema tri tela u ogranicenom slucaju moze pomoci boljem razumevanju dinamike tri tela u suncevom sistemu. U koordinatnom sistemu koji rotira, vezanim za dva primarna tela, postoje pet stacionarnih Lagrangevih tacaka. Jednacine kretanja treceg tela u blizini Lagranzeve tacke mogu biti linearizovane, I pod izvesnim uslovima pokazuju da moze postojati libraciono kretanje oko Lagranzevih tacaka. Prikazani su primeri numerickih resenja putanja oko Lagranzevih tacaka u inercijalnim I rotirajucim koordinatama. Primeri ukljucuju libracije, potkovicne orbite I haoticne orbite. Ograniceni problem tri tela, sa cetiri stepena slobode pruza znacajne mogucnosti za studentske projekte iz numericke fizike.