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Chaos in the one-dimensional gravitational three-body problem (1993).
| Content Provider | CiteSeerX |
|---|---|
| Author | Jarmo Hietarinta, A. |
| Abstract | We have investigated the appearance of chaos in the 1-dimensional Newtonian gravitational three-body system (three masses on a line with −1/r pairwise potential). In the center of mass coordinates this system has two degrees of freedom and can be conveniently studied using Poincaré sections. We have concentrated in particular on how the behavior changes when the relative masses of the three bodies change. We consider only the physically more interesting case of negative total energy. For two mass choices we have calculated 18000 full orbits (with initial states on a 100 × 180 lattice on the Poincaré section) and obtained dwell time distributions. For 105 mass choices we have calculated Poincaré maps for 10×18 starting points. Our results show that the Poincaré section (and hence the phase space) divides into three well defined regions with orbits of different characteristics: 1) There is a region of fast scattering, with a minimum of pairwise collisions. This region consists of ‘scallops ’ bordering the E = 0 line, within a scallop the orbits vary smoothly. The number of the scallops increases as the mass of the central particle decreases. 2) In the chaotic scattering region the interaction times are longer, and both the interaction time and the final state depend sensitively on the starting point on the Poincaré section. For both 1) and 2) the initial and final states consists of a binary + single particle. 3) The third region consists of quasiperiodic orbits where the three masses are bound together forever. At the center of the quasiperiodic region there is a periodic orbit discovered (numerically) by Schubart in 1956. The stability of the Schubart orbit turns out to correlate strongly with the global behavior. I. |
| File Format | |
| Publisher Date | 1993-01-01 |
| Access Restriction | Open |
| Subject Keyword | Poincar Section One-dimensional Gravitational Three-body Problem Interaction Time Mass Choice Binary Single Particle Relative Mass Dwell Time Distribution Final State Consists Interesting Case Central Particle Decrease Defined Region Mass Coordinate Fast Scattering Periodic Orbit Final State Depend Third Region Initial State Chaotic Scattering Region Negative Total Energy Full Orbit Quasiperiodic Region Behavior Change Global Behavior Schubart Orbit Poincar Map 1-dimensional Newtonian Gravitational Three-body System Quasiperiodic Orbit Different Characteristic Pairwise Potential Phase Space Pairwise Collision |
| Content Type | Text |
