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Stability of motion in Hill's sense in the problem of many bodies

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Abstract:

A criterion on the stability of motion due to Hill in the problem of many absolutely rigid bodies possessing an arbitrary form and structure of the density distribution is established. A graphical illustration of the results obtained is given for the case of three bodies. The instability in Hill's sense for the classical problem of n material points is shown. Conditions of possible disintegration of the n-body system when removing even one body to an infinitely large distance from another body are considered.

Keywords: Hill stability; Many-body problem; Mutual collisions

Document Type: Research Article

DOI: http://dx.doi.org/10.1080/1055679031000139433

Publication date: August 1, 2003

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