Abstract
We study the non-linear stability of the equilibria corresponding to the motion of a particle orbiting around a finite straight segment. The potential is a logarithmic function and may be considered as an approximation to the one generated by elongated celestial bodies. By means of the Arnold's theorem for non-definite quadratic forms we determine the orbital stability of the equilibria, for all values of the parameter k of the problem, resonant cases included.
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Riaguas, A., Elipe, A. & López-Moratalla, T. Non-linear stability of the equilibria in the gravity field of a finite straight segment. Celestial Mechanics and Dynamical Astronomy 81, 235–248 (2001). https://doi.org/10.1023/A:1013217913585
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DOI: https://doi.org/10.1023/A:1013217913585