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Stability of relative equilibria in the full two-body problem
1The University of Michigan, Ann Arbor, MI 48109-2140, USA. scheeres@umich.edu
Annals of the New York Academy of Sciences
|June 29, 2004
Summary
This study analyzes the stability of two massive bodies interacting, specifically an ellipsoid and a sphere. We characterized planar stability for relative equilibrium solutions, finding it depends on mass ratio and shape.
Area of Science:
- Celestial Mechanics
- Astrodynamics
- Gravitational Dynamics
Background:
- Understanding the stability of interacting massive bodies is crucial for space missions and celestial body dynamics.
- Previous research often simplified body shapes or focused on specific scenarios.
Purpose of the Study:
- To explore the stability of relative equilibrium solutions for the interaction between an ellipsoid and a sphere.
- To characterize planar stability across various parameter values like mass ratio and shape.
Main Methods:
- Reduced the dynamical problem to a two-degrees of freedom Hamiltonian system for planar motion.
- Efficiently computed stability characteristics of relative equilibria using the Hamiltonian system.
Main Results:
- Characterized planar stability for the ellipsoid-sphere system.
- Identified key parameters influencing stability: mass ratio, ellipsoid shape, and normalized distance.
Conclusions:
- The study provides a framework for understanding the stability of complex gravitational interactions.
- Further investigation into full stability is warranted for a comprehensive analysis.