1. Effect of Finite Straight Segment on the Non-linear Stability of the Equilibrium Point in the Planar Robe's Problem.
- Author
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Kaur, Bhavneet, Kumar, Sumit, and Aggarwal, Rajiv
- Subjects
LAGRANGIAN points ,EQUILIBRIUM ,THREE-body problem ,NONLINEAR equations ,EQUATIONS of motion ,NONLINEAR analysis - Abstract
In non-linear stability analysis, the effects of non-linear terms in the equations of motion are considered. The presence of these non-linear terms can cause the results of linear stability to change dramatically. Therefore, the Arnold–Moser theorem (Kolmogorov–Arnold–Moser theory) has been used to study the non-linear stability of the equilibrium point in the planar Robe's restricted three-body problem when the second primary is a finite straight segment of length . The density parameter is considered zero. The equilibrium point has been found to be stable in non-linear sense for all mass ratios in the range of linear stability except possibly for six critical values of the mass ratio . The critical values depend on the length parameter , which shows that the length parameter has significant effect on the non-linear stability of the equilibrium point. The obtained results are applied to predict the stability of equilibrium point for Jupiter–Amalthea system. It is observed that the equilibrium point is unstable for Jupiter‒Amalthea system. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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