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Trajectories of the plate-ball problem. (English) Zbl 1377.70023
Mladenov, Ivaïlo M. (ed.) et al., Proceedings of the 18th international conference on geometry, integrability and quantization, Sts. Constantine and Elena (near Varna), Bulgaria, June 3–8, 2016. Sofia: Avangard Prima. Geometry, Integrability and Quantization, 203-216 (2017).
Summary: The plate-ball problem concerns the shortest trajectories traced by a rolling sphere on a horizontal plane between the prescribed initial and final states meaning the positions and orientations of the sphere. Here we present an explicit parametric representation of these trajectories in terms of the Jacobian elliptic functions and elliptic integrals.
For the entire collection see [Zbl 1359.53005].
70E18 Motion of a rigid body in contact with a solid surface
70Q05 Control of mechanical systems
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