2025-03-20 ハーバード大学
＜関連情報＞
- https://seas.harvard.edu/news/2025/03/getting-ball-rolling
- https://www.pnas.org/doi/10.1073/pnas.2417161122
不規則な円柱と球体の圧延における相転移 Phase transitions in the rolling of irregular cylinders and spheres
Daoyuan Qian, Yeonsu Jung, and L. Mahadevan
Proceedings of the National Academy of Sciences Published:March 5, 2025
DOI:https://doi.org/10.1073/pnas.2417161122
Significance
While the nonslip rolling of regular objects such as spheres and cylinders is treated in all elementary physics textbooks, the rolling of irregular objects, which is arguably more interesting and relevant, is far less studied. We use a combination of theory, simulations, and experiments to study this problem. We uncover singular behavior at the onset of motion which arises due to the interplay between constrained dynamics and shape randomness in both 2D and 3D settings and corroborate our theoretical results with experiments. Our results are likely to be relevant for applications across scales for subjects that range from cellular transport to robotics.
Abstract
When placed on an inclined plane, a perfect 2D disk or 3D sphere simply rolls down in a straight line under gravity. But how is the rolling affected if these shapes are irregular or random? Treating the terminal rolling speed as an order parameter, we show that there are qualitative transitions in the speed as a function of the dimension of the state space and inertia. We calculate the scaling exponents and the macroscopic lag time associated with the presence of first- and second-order transitions and describe the regimes of coexistence of stable states and the accompanying hysteresis. Experiments with rolling cylinders corroborate our theoretical results on the scaling of the lag time. Experiments with spheres reveal closed orbits and their period-doubling in the overdamped and inertial limits, respectively, providing visible manifestations of the hairy ball theorem and the doubly connected nature of SO(3), the space of 3D rotations. Going beyond simple curiosity, our study might shed light on a number of natural and artificial systems that involve the rolling of irregular objects, ranging from nanoscale cellular transport to robotics.
