Gyrostats in free motion as a test bench of integrability and chaos.
- Elipe, A. 1
- Iñarrea, M. 2
- Lanchares, V. 2
- Arribas, M. 1
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1
Universidad de Zaragoza
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2
Universidad de La Rioja
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ISSN: 0065-3438
Year of publication: 2006
Volume: 122
Pages: 89-106
Type: Article
More publications in: Advances in the Astronautical Sciences
Abstract
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.
Funding information
Supported by the Spanish Ministry of Science and Technology (Projects # BFM2002-03157, # BFM2003-02137 and # ESP2002-02329).Funders
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Spanish Ministry of Science and Technology
- BFM2002-03157
- BFM2003-02137
- ESP2002-02329