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The existence and stability of “orbitally uniform” rotations of a vibrating dumbbell on an elliptic orbit

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Abstract

The problem of planar motions of a variable-length dumbbell-shaped body in the central field of the Newton attraction is considered. The rules of varying the dumbbell length, at which the dumbbell with respect to the true anomaly can rotate uniformly around the center of mass, are indicated for the equation of motion of the dumbbell written in a satellite approximation [1–8]. When fulfilling these rules, the necessary stability conditions of mentioned motions are investigated.

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Authors and Affiliations

  1. Dorodnitsyn Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119991, Russia

    A. A. Burov & I. I. Kosenko

Authors
  1. A. A. Burov
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  2. I. I. Kosenko
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Correspondence to A. A. Burov.

Additional information

Original Russian Text © A.A. Burov, I.I. Kosenko, 2013, published in Doklady Akademii Nauk, 2013, Vol. 451, No. 2, pp. 164–167.

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Burov, A.A., Kosenko, I.I. The existence and stability of “orbitally uniform” rotations of a vibrating dumbbell on an elliptic orbit. Dokl. Phys. 58, 305–308 (2013). https://doi.org/10.1134/S1028335813070069

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