# The reduction of the linear stability of elliptic Euler–Moulton solutions of the n-body problem to those of 3-body problems

@article{Zhou2015TheRO,
title={The reduction of the linear stability of elliptic Euler–Moulton solutions of the n-body problem to those of 3-body problems},
author={Qinglong Zhou and Yiming Long},
journal={Celestial Mechanics and Dynamical Astronomy},
year={2015},
volume={127},
pages={397-428}
}
• Published 31 October 2015
• Physics, Mathematics
• Celestial Mechanics and Dynamical Astronomy
In this paper, we consider the elliptic collinear solutions of the classical n-body problem, where the n bodies always stay on a straight line, and each of them moves on its own elliptic orbit with the same eccentricity. Such a motion is called an elliptic Euler–Moulton collinear solution. Here we prove that the corresponding linearized Hamiltonian system at such an elliptic Euler–Moulton collinear solution of n-bodies splits into $$(n-1)$$(n-1) independent linear Hamiltonian systems, the first… Expand
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