Shadowing unstable orbits of the Sitnikov elliptic 3-body problem

Abstract

Errors in numerical simulations of gravitating systems can be magnified exponentially over short periods of time. Numerical shadowing provides a way of demonstrating that the dynamics represented by numerical simulations are representative of true dynamics. Using the Sitnikov Problem as an example, it is demonstrated that unstable orbits of the 3-body problem can be shadowed for long periods of time. In addition, it is shown that the stretching of phase space near escape and capture regions is a cause for the failure of the shadowing refinement procedure.

9 pages, 13 figures, accepted in MNRAS

References in corpus (3)

• Instability of the Gravitational N-Body Problem in the Large-N Limit
• On the relationship between instability and Lyapunov times for the 3-body problem
• Shadowing high-dimensional Hamiltonian systems: the gravitational n-body problem

Cited by in corpus (3)

• On the minimal accuracy required for simulating self-gravitating systems by means of direct N-body methods
• Gargantuan chaotic gravitational three-body systems and their irreversibility to the Planck length
• Are long-term $N$-body simulations reliable?