A biased ball rolled and spun on a horizontal surface exhibits interesting dynamics. We investigate the motion of a truncated billiard ball, via experiments, analytical methods, and numerical solutions of the equations of motion for a biased sphere rolling without slipping. Solutions are identified where the center of mass moves in a circular or a square path, and we investigate other quasi-periodic motions of the ball.
REFERENCES
1.
M. N.
Brearley
and
B. A.
Bolt
, “
The dynamics of a bowl
,” Q. J. Mech. Appl. Math.
11
, 351
–363
(1958
).2.
M. N.
Brearley
, “
The motion of a biased bowl with perturbing projection conditions
,” Math. Proc. Cambridge Philos. Soc.
57
, 131
–151
(1961
).3.
Rod
Cross
, “
The trajectory of a ball in lawn bowls
,” Am. J. Phys.
66
, 735
–738
(1998
).4.
David P.
Jackson
,
David
Mertens
, and
Brett J.
Pearson
, “
Hurricane balls: A rigid-body-motion project for undergraduates
,” Am. J. Phys.
83
, 959
–968
(2015
).5.
H. K.
Moffatt
,
Y.
Shimomura
, and
M.
Branicki
, “
Dynamics of an axisymmetric body spinning on a horizontal surface. I. Stability and the gyroscopic approximation
,” Proc. R. Soc. London A
460
, 3643
–3672
(2004
).6.
Rod
Cross
, “
Spin experiments with a biased ball
,” Eur. J. Phys.
40
, 055003
(2019
).7.
A.
Kilin
and
E.
Pivovarova
, “
The rolling motion of a truncated ball without slipping and spinning on a plane
,” Regul. Chaotic Dyn.
22
, 298
–317
(2017
).8.
M. A.
Jalali
,
M. S.
Sarebangholi
, and
M.-R.
Alam
, “
Terminal retrograde turn of rolling rings
,” Phys. Rev. E
92
, 032913
(2015
).9.
A. V.
Borisov
,
A. A.
Kilin
, and
Y. L.
Karavaev
, “
Retrograde motion of a rolling disk
,” Phys. Usp.
60
, 931
–934
(2017
).10.
Cliff
Frohlich
, “
What makes bowling balls hook?
,” Am. J. Phys.
72
, 1170
–1177
(2004
).11.
Kevin
King
,
N. C.
Perkins
,
Hugh
Churchill
,
Ryan
McGinnis
,
Ryan
Doss
, and
Ron
Hickland
, “
Bowling ball dynamics revealed by miniature wireless MEMS inertial measurement unit
,” Sports Eng.
13
, 95
–104
(2011
).12.
Rod
Cross
, “
A hemispherical tippe top
,” Eur. J. Phys.
41
, 025001
(2020
).13.
W. H.
Press
,
B. P.
Flannery
,
S. A.
Teukolsky
, and
W. T.
Vetterling
, Numerical Recipes in C
, 2nd ed. (
Cambridge U. P
.,
New York
, 1992
).14.
See supplementary material at http://dx.doi.org/10.1119/10.0000905 for movies of the motion of the truncated billiard ball filmed at 300 fps. The visualisations produced by the code, as well as the supplementary videos, are at <http://www.physics.usyd.edu.au/∼wheat/biased-ball/>.
15.
E. T.
Whittaker
, A Treatise on the Analytical Dynamics of Particles and Rigid Bodies, 2nd
ed. (
Cambridge U. P
.,
Cambridge, UK
, 1917
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2020
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