Gyrostats in free motion as a test bench of integrability and chaos.

  1. Elipe, A. 1
  2. Iñarrea, M. 2
  3. Lanchares, V. 2
  4. Arribas, M. 1
  1. 1 Universidad de Zaragoza
    info

    Universidad de Zaragoza

    Zaragoza, España

    ROR https://ror.org/012a91z28

  2. 2 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

Revista:
Advances in the Astronautical Sciences

ISSN: 0065-3438

Año de publicación: 2006

Volumen: 122

Páginas: 89-106

Tipo: Artículo

SCOPUS: 2-s2.0-33646552663 WoS: WOS:000236528100006 GOOGLE SCHOLAR

Otras publicaciones en: Advances in the Astronautical Sciences

Resumen

We begin with the analysis of the attitude dynamics of a gyrostat under no external forces. We introduce suitable coordinates to represent the orbits of constant angular momentum as a flow on a sphere. With these coordinates, we prove that the problem is identical to a general class of Hamiltonian systems which are polynomials of at most degree two in a base of the Lie algebra SO(3). This problem results to be a generalization of the rigid body in free rotation and can be solved in terms of elliptic functions. However, small time-dependent perturbations can break integrability and the system exhibits chaotic behavior. Classical Melnikov analysis allows us to discover the existence of standard structures of chaotic systems, like stochastic layers and subharmonic resonances. Also chaos control can be achieved by means of spinning rotors and aerodynamic forces.

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Información de financiación

Supported by the Spanish Ministry of Science and Technology (Projects # BFM2002-03157, # BFM2003-02137 and # ESP2002-02329).

Financiadores

  • Spanish Ministry of Science and Technology
    • BFM2002-03157
    • BFM2003-02137
    • ESP2002-02329