Leveraging Discrete Variational Mechanics to Explore the Effect of an Autonomous Three-Body Interaction Added to the Restricted Problem
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With recent improvements in ground and space-based telescopes, a large number of binary systems have been observed both within the solar system and beyond. These systems can take the form of asteroid pairs or even binary stars, with each component possessing a similar mass. In this investigation, periodic motions near large mass ratio binaries are explored using the circular restricted three-body problem, which is modified to include an additional three-body interaction. Discrete variational mechanics is leveraged to obtain periodic orbits that exhibit interesting shape characteristics, as well as the corresponding natural parameters. Shape characteristics and structural changes are explained using the stability and existence of equilibrium points, enabling exploration of the effect of an additional three-body interaction and conditions for reproducibility in a natural gravitational environment.
KeywordsPeriodic Orbit Equilibrium Point Constrain Optimization Problem Dynamical System Theory Reference Path
The authors wish to acknowledge support from the Zonta International Amelia Earhart Fellowship during this work, as well as from the School of Aeronautics and Astronautics at Purdue University.
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