Related Experiment Video
Updated: Jun 8, 2026
11:03
An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
Hamiltonian intermittency and Lévy flights in the three-body problem
1Pulkovo Observatory of the Russian Academy of Sciences, St. Petersburg 196140, Russia. iis@gao.spb.ru
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 28, 2010
Summary
In hierarchical three-body systems, escaping bodies exhibit Lévy flights near disruption. This leads to heavy-tailed survival probability decay and a quasilinear relationship between Lyapunov and disruption times.
Area of Science:
- Celestial Mechanics
- Dynamical Astronomy
- Astrophysics
Background:
- The restricted three-body problem is fundamental to understanding gravitational interactions.
- Analyzing disruption and Lyapunov times provides insights into system stability and evolution.
Purpose of the Study:
- To investigate the statistical properties of disruption and Lyapunov times in hierarchical restricted three-body systems.
- To characterize the behavior of escaping bodies at the edge of disruption.
Main Methods:
- Statistical analysis of orbital periods and orbit sizes.
- Examination of survival probability decay and its power-law index.
- Correlation analysis between Lyapunov and disruption times.
Main Results:
- Escaping bodies exhibit Lévy flights at the edge of disruption.
- Survival probability decay follows a heavy-tailed distribution with a power-law index of -2/3.
- A quasilinear relationship exists between Lyapunov and disruption times.
Conclusions:
- Lévy flights are a key feature of chaotic dynamics in these systems.
- The findings offer a new perspective on three-body interactions and resonant scattering.
- Results are applicable to understanding complex gravitational dynamics.
Related Concept Videos
01:12Reduced Mass Coordinates: Isolated Two-body Problem
In classical mechanics, the two-body problem is one of the fundamental problems describing the motion of two interacting bodies under gravity or any other central force. When considering the motion of two bodies, one of the most important concepts is the reduced mass coordinates, a quantity that allows the two-body problem to be solved like a single-body problem. In these circumstances, it is assumed that a single body with reduced mass revolves around another body fixed in a position with an...
01:28Conservation of Linear Momentum for a System of Particles
In the dynamic realm of billiards, a fascinating interplay of forces governs the motion of cue balls and stationary balls. When the cue ball collides with a stationary ball, linear momentum is exchanged. The cue ball imparts a fraction of its linear momentum to the stationary ball, causing the cue ball to decelerate while initiating the motion of the stationary ball.
The impulsive force at play during this interaction is of extremely short duration, rendering its impulse negligible. When...
The impulsive force at play during this interaction is of extremely short duration, rendering its impulse negligible. When...
01:18First Law: Particles in Two-dimensional Equilibrium
Recall that a particle in equilibrium is one for which the external forces are balanced. Static equilibrium involves objects at rest, and dynamic equilibrium involves objects in motion without acceleration; but it is important to remember that these conditions are relative. For instance, an object may be at rest when viewed from one frame of reference, but that same object would appear to be in motion when viewed by someone moving at a constant velocity.
Newton's first law tells us about the...
Newton's first law tells us about the...
01:21Principle of Linear Impulse and Momentum for a System of Particles
In the context of a system of particles moving relative to an inertial frame of reference, the equation of motion is a crucial tool for understanding the dynamics of the system. This equation, which accounts for external forces acting on each particle, plays a fundamental role in describing the system's behavior.
Notably, internal forces between particles, occurring in equal and opposite collinear pairs, cancel out and are not part of the equation of motion. This exclusion simplifies the...
Notably, internal forces between particles, occurring in equal and opposite collinear pairs, cancel out and are not part of the equation of motion. This exclusion simplifies the...
01:22Eulerian and Lagrangian Flow Descriptions
Fluid flow analysis is critical in many scientific and engineering disciplines, and two principal approaches are used to describe this flow: the Eulerian and Lagrangian methods. These methods offer different perspectives on monitoring and analyzing the motion of fluids, each with distinct advantages depending on the scenario.
The Eulerian method focuses on fixed points in space where fluid properties, such as velocity, pressure, and temperature, are observed as the fluid moves between these...
The Eulerian method focuses on fixed points in space where fluid properties, such as velocity, pressure, and temperature, are observed as the fluid moves between these...
01:10First Law: Particles in One-dimensional Equilibrium
Newton's first law of motion states that a body at rest remains at rest, or if in motion, remains in motion at constant velocity, unless acted on by a net external force. It also states that there must be a cause for any change in velocity (a change in either magnitude or direction) to occur. This cause is a net external force. For example, consider what happens to an object sliding along a rough horizontal surface. The object quickly grinds to a halt, due to the net force of friction. If we...