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Rolling manifolds on space forms. (English) Zbl 1321.53021
The rolling problem without spinning nor slipping determines a dynamical system with complicated (fractal) properties. As a first step of the solution, the system is investigated at the level of kinematic motions using an appropriate affine connection. One says that the rolling problem is completely controllable, if for arbitrary two points in the configuration space there is a loop, along which the parallel transport joins the two states. In the paper, the question “if the rolling problem is controllable?” is reformulated in terms of curvature of the connection. This gives a sufficient condition of controllability and a description of the reachable set in a general case.

53B21 Methods of local Riemannian geometry
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