Spatial resonant rotations of a three-axis satellite with a ball damper in a circular orbit

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Resumo

For a three-axis satellite with a ball damper, resonant rotations in the central gravitational field are studied. The equations of the rotational motion of a satellite in an elliptical orbit are obtained. For the case of a circular orbit, spatial resonance rotations of 1 : 1 and 2 : 1 were investigated using the averaging method.

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Sobre autores

N. Amel’kin

Moscow Institute of Physics and Technology

Autor responsável pela correspondência
Email: namelkin@mail.ru
Rússia, Moscow

Bibliografia

  1. Beletskii V.V. Motion of a Satellite with Respect to Center of Mass in Gravitational Field. M.: Izd. MGU, 1975. 308 p. [in Russian].
  2. Markeev A.P. Linear Hamiltonian systems and some problems about the stability of the satellite motion relative to the center of mass. M. Izhevsk: Research Center “Regular and chaotic dynamics”, 2009. 396 p. [in Russian].
  3. Chernous’ko F.L. Resonance phenomena in the motion of the satellite relative to the center of mass // J. Comput. Math. Math. Phys. 1963. V. 3. № 3. P. 528–538 [in Russian].
  4. Amel’kin N.I., Kholoshchak V.V. Evolution of the rotational movement of a dynamically symmetric satellite with inner damping in a circular orbit // Mech. Solids. 2019. V. 54. № 2. P. 179–189. https://doi.org/10.3103/S0025654419030014
  5. Amel’kin N.I., Kholoshchak V.V. Rotational motion of a non-symmetrical satellite with a damper in a circular orbit // Mech. Solids. 2019. V. 54. № 2. P. 190–203. https://doi.org/10.3103/S0025654419030026
  6. Amel’kin N.I. Evolution of rotational motion of the planet Earth under the influence of internal dissipative forces // Cosmic Research. 2023. V. 61. № 6. P. 510–521. https://doi.org/10.1134/S001095252370051X
  7. Amel’kin N.I. On the plane resonant rotations of a satellite with a spherical damper in an elliptical orbit // Mech. Solids. 2022. V. 57. № 7. P. 1644–1656. https://doi.org/10.31857/S003282352203002X
  8. Amel’kin N.I. Resonant rotations of a dynamically symmetric satellite with a spherical damper in a circular orbit // Mech. Solids. 2024. V. 59. № 3. P. 1266–1282. https://doi.org/10.1134/S0025654424602908X
  9. Bogolyubov N.N., Mitropol’skii Yu.A. Asymptotic Methods for Theory of Nonlinear Oscillations. M.: Nauka, 1974 [in Russian].
  10. Zhuravlev V.Ph., Klimov D.M. Applied Methods for Oscillations Theory. M.: Nauka, 1988 [in Russian].
  11. Tikhonov A.N. Systems of differential equations containing small parameters at derivatives // Math. collection. 1952. V. 73. № 3. P. 575–586 [in Russian].

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2. Fig. 1. Beletsky-Chernousko variables.

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3. Fig. 2. Phase trajectories.

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4. Fig. 3. Resonant rotations 2:1.

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5. Fig. 4. Resonant rotations 1:1.

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