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The problem of a disc or cylinder initially rolling with slipping on a surface and subsequently transitioning to rolling without slipping is often cited in textbooks. The following experiment serves to clearly demonstrate the transition…
The horizontal dynamics of a bouncing ball interacting with an irregular surface is investigated and is found to demonstrate behavior analogous to a random walk. Its stochastic character is substantiated by the calculation of a permutation…
Spin plays a pivotal role in ball-based sports. Estimating spin becomes a key skill due to its impact on the ball's trajectory and bouncing behavior. Spin cannot be observed directly, making it inherently challenging to estimate. In table…
Tracking the ball is critical for video-based analysis of team sports. However, it is difficult, especially in low-resolution images, due to the small size of the ball, its speed that creates motion blur, and its often being occluded by…
We consider systems of "pinned balls," i.e., balls that have fixed positions and pseudo-velocities. Pseudo-velocities change according to the same rules as those for velocities of totally elastic collisions between moving balls. The times…
In this work, we present an analysis tool to help golf beginners compare their swing motion with experts' swing motion. The proposed application synchronizes videos with different swing phase timings using the latent features extracted by a…
Putting several hard balls into a two-dimensional bowl can form a very basic two-dimensional model of hard-ball system. When the two-dimensional bowl has a parallel-rotation at a uniform speed around a center, when the number of balls is…
The drag on a golf ball can be reduced by dimpling the surface. There have been few studies, primarily experimental, that provide quantitative information on the details of the drag reduction mechanisms. To illuminate the underlying…
Current exergaming sensors and inertial systems attached to sports equipment or the human body can provide quantitative information about the movement or impact e.g. with the ball. However, the scope of these technologies is not to…
Prunning front is calculated for a bouncing ball system and the results are compared to a braid analysis. To Appear in Physical Review E.
Sound can complement vision in ball sports by providing subtle cues about contact dynamics. In table tennis, the brief, high-frequency sounds produced during racket-ball impacts carry information about the racket type, the surface…
A ball rolled over a shallow step will experience an increase in velocity along the direction perpendicular to the step. This causes a deflection in the ball's trajectory. In this paper we derive the equations that describe the motion of a…
If a tennis ball is held above a basket ball with their centers vertically aligned, and the balls are released to collide with the floor, the tennis ball may rebound at a surprisingly high speed. We show in this article that the simple…
Using videos to analyze pitchers in baseball can play a vital role in strategizing and injury prevention. Computer vision-based pose analysis offers a time-efficient and cost-effective approach. However, the use of accessible broadcast…
Experiments on the motion of a particle on an inclined rough plane have yielded some surprising results. For example, it was found that the frictional force acting on the ball is viscous, {\it i.e.} proportional to the velocity rather than…
Wind-blown sand, or "saltation", ejects dust aerosols into the atmosphere, creates sand dunes, and erodes geological features. We present a comprehensive numerical model of steady-state saltation that, in contrast to most previous studies,…
Evolutionary motions in a bouncing ball system consisting of a ball having a free fall in the Earth's gravitational field have been studied systematically. Because of nonlinear form of the equations of motion, evolutions show chaos for…
Estimating win probability is one of the classic modeling tasks of sports analytics. Many widely used win probability estimators use machine learning to fit the relationship between a binary win/loss outcome variable and certain game-state…
By means of Molecular Dynamics simulations, we investigate the elementary process of avalanches and size segregation by surface flow in 2 dimensions: a single ball confined to moving along an inclined line consisting of balls. The global…
Control of a hybrid dynamical system can manifest in one of two main ways: either through the continuous or the discrete dynamics. An example of controls influencing the continuous dynamics is legged locomotion, where the joints are…