Gyrostats in free motion as a test bench of integrability and chaos.
- Elipe, A. 1
- Iñarrea, M. 2
- Lanchares, V. 2
- Arribas, M. 1
-
1
Universidad de Zaragoza
info
-
2
Universidad de La Rioja
info
ISSN: 0065-3438
Argitalpen urtea: 2006
Alea: 122
Orrialdeak: 89-106
Mota: Artikulua
Beste argitalpen batzuk: Advances in the Astronautical Sciences
Laburpena
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.
Finantzaketari buruzko informazioa
Supported by the Spanish Ministry of Science and Technology (Projects # BFM2002-03157, # BFM2003-02137 and # ESP2002-02329).Finantzatzaile
-
Spanish Ministry of Science and Technology
- BFM2002-03157
- BFM2003-02137
- ESP2002-02329