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A criterion for the linear stability of theequilibrium points in the perturbed restricted three-body problem and its application in Robe's problem |
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| Authors: | Shu Si-hui Lu Ben-kui Chen Wu-shen Liu Fu-yao |
| Institution: | 1Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing 210008, China 2National Astronomical Observatories, Chinese Academy of Sciences, Beijing 100012, China 3Jianxi Teachers' College of Science and Technology, Nanchang 330013, China 4Nanjing University of Technology, Nanjing 210027, China |
| Abstract: | A criterion for the linear stability of the equilibrium points in the perturbed restricted three-body problem is given. This criterion is related only to the coefficients of the characteristic equation of the tangent map of an equilibrium point, and this is convenient to use. With this criterion, we have discussed the linear stability of the equilibrium points in the Robe problem under the perturbation of a drag force, derived the linearly stable region of the equilibrium point in the perturbed Robe's problem with the drag given by Hallen et al., and improved as well the results obtained by Giordano et al. |
| Keywords: | celestial mechanics |
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