Modelling and simulation of a sphere rolling on the inside of a rough vertical cylinder

W. Blajer and K. Kołodziejczyk

Mathematical and Computer Modelling of Dynamical Systems, 2006, vol. 12, issue 6, 543-553

Abstract: A classical problem of nonholonomic system dynamics—the motion of a sphere on the inside of a rough vertical cylinder—is extended to rolling friction. The case study is modelled in independent coordinates. Due to the nonholonomic constraints imposed on the sphere, the governing equations arise as a set of differential-algebraic equations. The results of numerical simulations show the transition of the sphere from a sinusoid path on the vertical cylinder surface to a fall with slip. The physics of the ‘paradoxical’ motion is explained in detail.

Date: 2006
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DOI: 10.1080/13873950500098747

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