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Non-holonomic distributions and dynamical systems

We study a nonlinear dynamical model defined in terms of a
non-holonomic distribution $\Delta$ of polynomial vector fields,
satisfying the bracket generating condition of control theory. The
case when the Lie algebra $\mbox{span}(\Delta)$ is nilpotent is
discussed. In low dimensional cases, the step-2 models classical
particles in homogeneous magnetic fields whereas the step-3 models the
case of linear fields.
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