Null-forms of conic systems in $\mathbb{R}^3$ are determined by their symmetries
Résumé
We address the problem of characterisation of null-forms of conic $3$-dimensional systems, that is, control-affine systems whose field of admissible velocities forms a conic (without parameters) in the tangent space. Those systems have been previously identified as the simplest control systems under a conic nonholonomic constraint or as systems of zero curvature. In this work, we propose a direct characterisation of null-forms of conic systems among all control-affine systems by studying the Lie algebra of infinitesimal symmetries. Namely, we show that the Lie algebra of infinitesimal symmetries characterises uniquely null-forms of conic systems.
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Licence : CC BY NC SA - Paternité - Pas d'utilisation commerciale - Partage selon les Conditions Initiales
Licence : CC BY NC SA - Paternité - Pas d'utilisation commerciale - Partage selon les Conditions Initiales