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Published on: March 3, 2017
Chaos in the one-dimensional gravitational three-body problem
Jarmo Hietarinta1, Seppo Mikkola
1Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545Department of Physics, University of Turku, 20500 Turku, Finland(a))Turku University Observatory, 21500 Piikkio, Finland Department of Physics, University of Turku, 20500 Turku, Finland.
Chaos (Woodbury, N.Y.)
|April 1, 1993
Summary
Chaos emerges in the 1D Newtonian three-body system, with Poincare sections revealing distinct regions of fast scattering, chaotic scattering, and quasiperiodic orbits. Mass variations significantly influence orbital behavior and system dynamics.
Area of Science:
- Celestial Mechanics
- Astrophysics
- Dynamical Systems
Background:
- The Newtonian three-body problem is a classic challenge in physics, known for complex dynamics.
- Investigating chaos in simplified systems like the 1D gravitational case provides fundamental insights.
Purpose of the Study:
- To explore the emergence and characteristics of chaos in a one-dimensional Newtonian gravitational three-body system.
- To analyze how changes in relative masses affect the system's dynamics and phase space structure.
- To identify and differentiate distinct orbital behaviors within the system.
Main Methods:
- Utilized Poincare sections to analyze the two-degree-of-freedom system in center-of-mass coordinates.
- Calculated numerous full orbits and Poincare maps for various mass configurations and initial conditions.
- Examined dwell time distributions and phase space partitioning.
Main Results:
- Identified three distinct regions in the Poincare section: fast scattering, chaotic scattering, and quasiperiodic orbits.
- Observed that the number of 'scallops' in the fast scattering region increases as the central particle's mass decreases.
- Found that chaotic scattering exhibits sensitive dependence on initial conditions, with binary + single particle final states.
- Located quasiperiodic orbits, including Schubart's 1956 periodic orbit, whose stability correlates with global behavior.
Conclusions:
- The phase space of the 1D Newtonian three-body system is clearly divided into regions with distinct dynamical behaviors.
- Relative masses play a crucial role in determining the extent and nature of chaotic and regular motion.
- The stability of central periodic orbits is a strong indicator of the overall system dynamics.
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