Related papers: Three Balls Problem Revisited - On the Limitations…
Motion blur reduces the clarity of fast-moving objects, posing challenges for detection systems, especially in racket sports, where balls often appear as streaks rather than distinct points. Existing labeling conventions mark the ball at…
We give a new and elementary proof that the number of elastic collisions of a finite number of balls in the Euclidean space is finite. We show that if there are $n$ balls of equal masses and radii 1, and at the time of a collision between…
Ball and hoop system is a well-known model for the education of linear control systems. In this paper, we have a look at this system from another perspective and show that it is also suitable for demonstration of more advanced control…
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…
Consider the system of $n$ identical hard balls in $\mathbb R^3$ moving freely and colliding elastically. We show that there exist initial conditions such that the number of collisions is exponential in $n$.
We report on quasi-two-dimensional granular systems in which either one or two large balls is fluidized by an upflow of air in the presence of a background of several hundred smaller beads. A single large ball is observed to propel…
We propose a complete theoretical description of the tennis racket effect, which occurs in the free rotation of a three-dimensional rigid body. This effect is characterized by a flip ($\pi$- rotation) of the head of the racket when a full…
We analyze the impact of two equal billiard balls in three ideal situations: when the balls freely slide on the plane of the billiard, when they roll without sliding and when one of them freely slides and the other rolls. In all the cases…
We study the dynamics of three elastic particles in a finite interval where two light particles are separated by a heavy ``piston''. The piston undergoes surprisingly complex motion that is oscillatory at short time scales but seemingly…
We present a complete solution to the so-called tennis ball problem, which is equivalent to counting lattice paths in the plane that use North and East steps and lie between certain boundaries. The solution takes the form of explicit…
In this article, we consider a configuration of weighted random balls in $\mathbb{R}^d$ generated according to a Poisson point process. The model investigated exhibits inhomogeneity, as well as dependence between the centers and the radii…
Nonlinear dynamics of a bouncing ball moving in gravitational field and colliding with a moving limiter is considered. Several simple models of table motion are studied and compared. Dependence of displacement of the table on time,…
The tennis racket effect is a geometric phenomenon which occurs in a free rotation of a three-dimensional rigid body. In a complex phase space, we show that this effect originates from a pole of a Riemann surface and can be viewed as a…
When two identical balls collide with equal inital speed on a horizontal groove, one can observe three trajectory types depending on the groove width. To explain this observation, we derive velocity diagrams of the balls motions from…
Obtaining the precise 3D motion of a table tennis ball from standard monocular videos is a challenging problem, as existing methods trained on synthetic data struggle to generalize to the noisy, imperfect ball and table detections of the…
A simple model is applied to study a high temperature rather dense plasma ball. It is assumed that the ions and delocalized electrons are distributed uniformly throughout the ball, and extra/missing charge is found in a thin layer on the…
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…
We present a deep-dive into a real-world robotic learning system that, in previous work, was shown to be capable of hundreds of table tennis rallies with a human and has the ability to precisely return the ball to desired targets. This…
The zero-temperature limit of the backgammon model under resetting is studied. The model is a balls-in-boxes model whose relaxation dynamics is governed by the density of boxes containing just one particle. As these boxes become rare at…
Several scenarios used in teaching feature a rolling motion with slipping that transitions to one without through friction with the ground. We summarise these transitions by introducing an unknown impulse that is transferred to the ground.…