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On the planar motion in the full two-body problem with inertial symmetry
Authors:Pamela Woo  Arun K. Misra  Mehdi Keshmiri
Affiliation:1. Department of Mechanical Engineering, McGill University, Montreal, Canada
2. Department of Mechanical Engineering, Isfahan University of Technology, Isfahan, Iran
Abstract:Relative motion of binary asteroids, modeled as the full two-body planar problem, is studied, taking into account the shape and mass distribution of the bodies. Using the Lagrangian approach, the equations governing the motion are derived. The resulting system of four equations is nonlinear and coupled. These equations are solved numerically. In the particular case where the bodies have inertial symmetry, these equations can be reduced to a single equation, with small nonlinearity. The method of multiple scales is used to obtain a first-order solution for the reduced nonlinear equation. The solution is shown to be sufficient when compared with the numerical solution. Numerical results are provided for different example cases, including truncated-cone-shaped and peanut-shaped bodies.
Keywords:
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