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Chaotic motion around prolate deformed bodies.
1Departamento de Matemática Aplicada, Instituto de Matemática, Estatística e Computação Científica, Universidade Estadual de Campinas, 13083-970, Campinas, SP, Brazil. gueron@ime.unicamp.br
Summary
Particle motion near an attraction center with quadrupole deformation exhibits chaotic behavior. Increasing quadrupole deformation intensifies orbital instability, with implications for general relativity analogs.
Area of Science:
- Classical Mechanics
- Astrophysics
- Dynamical Systems
Background:
- Investigates particle dynamics under central forces with non-spherical potentials.
- Considers forces derived from monopolar and prolate quadrupole terms.
- Explores the transition from regular to chaotic motion.
Purpose of the Study:
- To analyze particle motion in an axially symmetric force field.
- To determine the influence of quadrupole deformation on orbital stability.
- To identify conditions leading to chaotic trajectories.
Main Methods:
- Utilizes Poincaré surface of sections for phase space visualization.
- Employs Lyapunov characteristic numbers to quantify chaos.
- Compares results with general relativistic analogs.
Main Results:
- Chaotic motion is observed for specific parameter ranges.
- Orbital instability demonstrably increases with the quadrupole parameter.
- The study reveals a direct correlation between quadrupole strength and chaotic behavior.
Conclusions:
- Axially symmetric potentials with quadrupole deformation can induce significant chaotic dynamics.
- Quadrupole effects are crucial for understanding orbital stability in non-spherical systems.
- Findings provide a foundation for exploring relativistic effects in similar systems.