Dynamics of a biased ball

Biased balls which roll without slipping exhibit interesting dynamics. Here are some examples, as animated gifs. The simulations use the parameters for a truncated billiard ball, which is 25.4 mm in radius, and which has had the top 12mm removed, leaving a flat top. The truncation displaces the center of mass by about 2.9mm from the geometric center of the ball.

In each animation the red lines indicate the path of the center of mass, and the blue and black lines correspond to the center of the flat top, and a point a further 25mm along the symmetry axis, respectively.

Supplementary videos (.mov files) are also provided in four cases, showing the motion of a real truncated billiard ball. The ball was filmed at 300 frames per second.

Animated gif Animated gif
The "lawn bowls mode". The ball rolls in a perfect circle, with a constant angle of inclination.
Supplementary video 1.
Approximately linear center-of-mass motion, with the symmetry axis of the ball nearly horizontal, and rapid precession.
Supplementary video 2.
Animated gif Animated gif
An approximately circular center-of-mass motion
Supplementary video 3.
A second approximately circular center-of-mass motion.
Animated gif Animated gif
The center of mass almost describes a square.
Supplementary video 4.
The center of mass almost describes a triangle.



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