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An intrinsic formulation of the problem on rolling manifolds. (English) Zbl 1261.37027
The present paper presents an intrinsic formulation of the kinematic problem of two \(n\)-dimensional manifolds, one rolling on the other one without twisting or slipping. The authors compare the intrinsic point of view versus the extrinsic one. They also show that the kinematic system of an \(n\)-dimensional sphere rolling over \({\mathbb R}^n\) is controllable. In contrast with this, the authors show that in the case \(\text{SE}(3)\) rolling over \(\text{se}(3)\), the system is not controllable.

MSC:
37J60 Nonholonomic dynamical systems
53A17 Differential geometric aspects in kinematics
70E18 Motion of a rigid body in contact with a solid surface
70Q05 Control of mechanical systems
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