The Lagrange-Jacobi equation in the finite-size many-body problem |
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Authors: | L. G. Luk’yanov L. P. Nasonova G. I. Shirmin |
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Affiliation: | (1) Sternberg Astronomical Institute, Universitetskii pr. 13, Moscow, 119992, Russia |
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Abstract: | We determine the values of the barycentric energy constant that necessarily result in collisions between bodies. The standard Hill stability regions in the problem of four or more bodies are shown to be located inside the regions where collisions are inevitable. Only in the problem of three finite bodies is part of the Hill stability region preserved where the bodies can move without colliding with one another. We point out possible astronomical applications of our results. |
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Keywords: | celestial mechanics many-body problems Lagrange-Jacobi equation Hill stability body collisions |
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