On the Stability of a Class of Permanent Rotations of a Heavy Asymmetric Gyrostat

  1. Iñarrea, M. 1
  2. Lanchares, V. 1
  3. Pascual, A.I. 1
  4. Elipe, A. 2
  1. 1 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

  2. 2 Centro Universitario de la Defensa de Zaragoza, Spain
Revista:
Regular and Chaotic Dynamics

ISSN: 1560-3547

Año de publicación: 2017

Volumen: 22

Número: 7

Páginas: 824-839

Tipo: Artículo

DOI: 10.1134/S156035471707005X SCOPUS: 2-s2.0-85042508362 WoS: WOS:000425980500005 GOOGLE SCHOLAR

Otras publicaciones en: Regular and Chaotic Dynamics

Proyectos relacionados

Sistemas dinámicos hamiltonianos: métodos y aplicaciones en física atómica y molecular y otros campos de interes. Hamiltonian dynamical systems: methods and applications in atomic and molecular physics and other fields of interest.

2015/00070/001

Resumen

We consider the motion of an asymmetric gyrostat under the attraction of a uniform Newtonian field. It is supposed that the center of mass lies along one of the principal axes of inertia, while a rotor spins around a different axis of inertia. For this problem, we obtain the possible permanent rotations, that is, the equilibria of the system. The Lyapunov stability of these permanent rotations is analyzed by means of the Energy–Casimir method and necessary and sufficient conditions are derived, proving that there exist permanent stable rotations when the gyrostat is oriented in any direction of the space. The geometry of the gyrostat and the value of the gyrostatic momentum are relevant in order to get stable permanent rotations. Moreover, it seems that the necessary conditions are also sufficient, but this fact can only be proved partially. © 2017, Pleiades Publishing, Ltd.