Degenerate abnormal trajectories in a sub-Riemannian problem with growth vector (2, 3, 5, 8)

We consider the nilpotent sub-Riemannian problem with growth vector (2, 3, 5, 8). We describe and study abnormal extremals orthogonal to the cube of the distribution. We analyze the geometric properties of a two-dimensional surface in the state space on which the corresponding abnormal trajectories...

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Veröffentlicht in:	Differential equations 2017-03, Vol.53 (3), p.352-365
Hauptverfasser:	Sachkov, Yu. L., Sachkova, E. F.
Format:	Artikel
Sprache:	eng
Schlagworte:	Algebra Control Theory Cubes Difference and Functional Equations Differential equations Geometry Lie groups Mathematical analysis Mathematics Mathematics and Statistics Optimization Ordinary Differential Equations Partial Differential Equations Studies Synthesis Trajectories Trajectory analysis Two-dimensional analysis
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Beschreibung
Zusammenfassung:	We consider the nilpotent sub-Riemannian problem with growth vector (2, 3, 5, 8). We describe and study abnormal extremals orthogonal to the cube of the distribution. We analyze the geometric properties of a two-dimensional surface in the state space on which the corresponding abnormal trajectories define optimal synthesis.
ISSN:	0012-2661 1608-3083
DOI:	10.1134/S0012266117030077