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math.DG2019
Geometric control theory of vertical rolling disc using symmetries
Jaroslav Hrdina, Ales Navrat, Lenka Zalabova
We use the methods of geometric control theory to study extremal trajectories of vertical rolling disk. We focus on the role of symmetries of the underlying geometric structures. W…
math.DG2018
Local geometric control of a certain mechanism with the growth vector (4,7)
Jaroslav Hrdina, Lenka Zalabova
We study local control of the mechanism with the growth vector (4,7). We study controllability and extremal trajectories on the nilpotent approximation as an example of the control…
math.DG2005
Generalized planar curves and quaternionic geometry
Jaroslav Hrdina, Jan Slovak
Motivated by the analogies between the projective and the almost quaternionic geometries, we study the generalized planar curves and mappings. We follow, recover, and extend the cl…