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The Dynamics of a Ball Rolling on a Rotating Plane
Author(s) -
Holden J. T.,
King A. C.
Publication year - 1990
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19900700825
Subject(s) - ball (mathematics) , drag , circular orbit , rolling resistance , plane (geometry) , classical mechanics , horizontal plane , physics , mechanics , orbital plane , rotation (mathematics) , viscous liquid , mathematics , inclined plane , orbit (dynamics) , equations of motion , dynamics (music) , geometry , engineering , mechanical engineering , quantum mechanics , aerospace engineering , acoustics
In the absence of any viscous or rolling resistance, a ball set on a uniformly rotating horizontal plane does not leave the plane but moves in a circular orbit. The equations of motion, when both viscous drag and rolling resistance are present, were set up by Fufaev [1] and Abdelkader [2] obtained a complicated implicit solution of the equations. In this paper we show that solutions may be found explicitly. The solutions depend on two parameters which determine whether the ball spirals towards, or away from, the axis of rotation, onto a circular orbit, or onto a fixed point.