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Shadowing high-dimensional hamiltonian systems: the gravitational N-body problem
1Department of Computer Science, University of Toronto, Ontario, M5S 3G4 Canada. wayne@cs.toronto.edu
Physical Review Letters
|March 14, 2003
Summary
Researchers explored "shadows," exact solutions to chaotic systems, in gravitational N-body problems. Shadows in softened potentials allow long-term analysis, unlike those in unsoftened potentials which are very short.
Area of Science:
- Astrophysics and computational physics.
Background:
- Chaotic systems, like the gravitational N-body problem, are challenging to solve numerically.
- Shadows represent exact solutions that closely track numerical computations for extended periods.
Purpose of the Study:
- To investigate the existence and duration of shadows in numerically computed solutions of the gravitational N-body problem.
- To determine the influence of potential type (softened vs. unsoftened) on shadow duration.
Main Methods:
- Numerical integration of the gravitational N-body problem using a variable-order, variable-time-step integrator.
- Systematic search for "shadow" solutions with the longest possible durations.
Main Results:
- Shadows were found to persist for significant durations in "softened" potentials, enabling the study of long-term system evolution.
- In contrast, "unsoftened" potentials resulted in very short shadow durations, limiting their utility for long-term analysis.
Conclusions:
- The presence of softened potentials is crucial for finding long-lived shadows in chaotic gravitational systems.
- Shadows offer a potential avenue for studying chaotic dynamics, but their applicability is highly dependent on the system's potential characteristics.
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