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The gyroscopic stability of the triangular stationary solutions of the generalized planar three-body problem

โœ Scribed by A.A. Burov; M. Pascal; S.Ya. Stepanov

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
799 KB
Volume
64
Category
Article
ISSN
0021-8928

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โœฆ Synopsis

The gyroscopic stability of the triangular solutions is investigated for the generalized planar three-body problem (point masses) which differs from the classical three-body problem by the addition of a weightless elastic tether connecting two of the three bodies. It is shown that, when the tether has low stiffness and the masses of the connected bodies are substantially different, the triangular motions are stable for any values of the remaining parameters of the system.

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A numerical study of asymmetric periodic solutions of the planar general three body problem is presented. The equations of variation are integrated numerically and the algorithms for the numerical determination of families of such periodic orbits are given. These orbits refer to a rotating frame of