Exact solution of a triaxial gyrostat with one rotor

  1. Elipe, A. 1
  2. Lanchares, V. 2
  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

Zeitschrift:
Celestial mechanics & dynamical astronomy

ISSN: 0923-2958

Datum der Publikation: 2008

Ausgabe: 101

Nummer: 1-2

Seiten: 49-68

Art: Artikel

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DOI: 10.1007/S10569-008-9129-6 SCOPUS: 2-s2.0-45449093377 WoS: WOS:000256427000004 GOOGLE SCHOLAR

Andere Publikationen in: Celestial mechanics & dynamical astronomy

Institutionelles Repository: lock_openOpen Access Editor

Zusammenfassung

The problem of the attitude dynamics of a triaxial gyrostat under no external torques and one constant internal rotor, is a three degrees-of-freedom system, although thanks to the existence of integrals of motion it can be reduced to only one degree-of-freedom problem. We introduce coordinates to represent the orbits of constant angular momentum as a flow on a sphere. This representation shows that the problem is equivalent to a quadratic Hamiltonian depending on two parameters. We find the exact solution of the orbits in terms of elliptic functions. By making use of properties of elliptic functions we find the solution at each region of the parametric partition from the solution of one region. We also prove that heteroclinic orbits are planar curves. © 2008 Springer Science+Business Media B.V.