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How to control Chaplygin’s sphere using rotors. (English) Zbl 1264.37016
The paper studies the controllability of a dynamically non-symmetric balanced sphere moving over a plane. Internal rotors are used as a mechanism for control. The no-slip condition at the point of contact is assumed. The algebraic controllability is shown and the control inputs that steer the ball along a given trajectory on the plane are found. For some simple trajectories, explicit tracking algorithms are proposed.

37J60 Nonholonomic dynamical systems
37J35 Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests
70E18 Motion of a rigid body in contact with a solid surface
70F25 Nonholonomic systems related to the dynamics of a system of particles
70H45 Constrained dynamics, Dirac’s theory of constraints
Full Text: DOI
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