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 in the direction of the angular momentum vector can wander, for no matter how small the potential is, 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.
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