The Influence of the Mass Ratio and the Jacobi Constant on the Probability of Escape in the 3D (4+2)-Body Ring Problem

The Influence of the Mass Ratio and the Jacobi Constant on the Probability of Escape in the 3D (4+2)-Body Ring Problem

The dynamics of escape in the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>N</mi><mo>+</mo><mn>2</mn><mo>)</mo></mrow><...

Full description

Saved in:
Bibliographic Details
Main Authors: Zahra Boureghda, Mari Carmen Martínez-Belda, Juan F. Navarro
Format: Article
Language:English
Published: MDPI AG 2025-06-01
Series:Mathematics
Subjects:
probability
N-body ring problem
fast escape
dynamical system
equations of motion
Online Access:https://www.mdpi.com/2227-7390/13/12/1992
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:The dynamics of escape in the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>N</mi><mo>+</mo><mn>2</mn><mo>)</mo></mrow></semantics></math></inline-formula>-body ring problem exhibits a limited supply of research that involves the investigation in the three-dimensional scenario. In this paper, we introduce a new method based on the use of a spherical surface of section to analyze the probability of escape in the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mn>4</mn><mo>+</mo><mn>2</mn><mo>)</mo></mrow></semantics></math></inline-formula>-body ring problem in three dimensions. Our analysis reveals perplexing results regarding the impact of the mass ratio, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>β</mi></semantics></math></inline-formula>, and the Jacobi constant, <i>C</i>, parameters on this escape probability. In order to delineate the different effects exerted by these parameters, we incorporate into the system three increasing values of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>β</mi></semantics></math></inline-formula> and four values of <i>C</i> for each value of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>β</mi></semantics></math></inline-formula>, that show different behaviors in the distribution of the escaping orbits.
ISSN:2227-7390

Similar Items