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November  2002, 2(4): 521-540. doi: 10.3934/dcdsb.2002.2.521

Regular and chaotic motions of the fast rotating rigid body: a numerical study

Giancarlo Benettin 1, , Anna Maria Cherubini 2, and  Francesco Fassò 3,

1. 

Università di Padova, Dipartimento di Matematica Pura e Applicata, INFM and GNFM, Via G. Belzoni 7, 35131 Padova, Italy
2. 

Università di Lecce, Dipartimento di Matematica and GNFM, Via per Arnesano, 73100 Lecce, Italy
3. 

Università di Padova, Dipartimento di Matematica Pura e Applicata and GNFM, Via G. Belzoni 7, 35131 Padova, Italy

Received  November 2001 Revised  May 2002 Published  August 2002

We numerically investigate the dynamics of a symmetric rigid body with a fixed point in a small analytic external potential (equivalently, a fast rotating body in a given external field) in the light of previous theoretical investigations based on Nekhoroshev theory. Special attention is posed on "resonant" motions, for which the tip of the unit vector $\mu$ in the direction of the angular momentum vector can wander, for no matter how small $\varepsilon$, on an extended, essentially two-dimensional, region of the unit sphere, a phenomenon called "slow chaos". We produce numerical evidence that slow chaos actually takes place in simple cases, in agreement with the theoretical prediction. Chaos however disappears for motions near proper rotations around the symmetry axis, thus indicating that the theory of these phenomena still needs to be improved. An heuristic explanation is proposed.
Keywords: Nekhoroshev theory, chaotic dynamics, Rigid body, symplectic integrators..
Mathematics Subject Classification: 70E17, 65P10, 37J4.
Citation: Giancarlo Benettin, Anna Maria Cherubini, Francesco Fassò. Regular and chaotic motions of the fast rotating rigid body: a numerical study. Discrete & Continuous Dynamical Systems - B, 2002, 2 (4) : 521-540. doi: 10.3934/dcdsb.2002.2.521
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