Related papers: Cycloid Experiment for freshmen physics labs
We prove some partial results on the periodicity of billiard systems on graphs. The results specialize to the case of $n$ billiards with equal mass on the unit interval or circle traveling at the same speed.
Students in introductory physics courses struggle to understand virtual image formation by a plane mirror and the proper construction of ray diagrams. This difficulty, if not sufficiently addressed, results in further problems throughout…
We study the rolling motion of a small solid sphere on a surface patterned rubber substrate in an external field with and without a noise. In the absence of the noise, the ball does not move below a threshold force above which it…
A widely used mathematical model for the bouncing motion of an ideally elastic ball -- referred to in previous work by the first two authors and collaborators as a {\em no-slip billiard} system -- exhibits some notable dynamical behavior…
In the curved spacetime background, the trajectory of a spinning test particle will deviate from the geodesic. Using the effective potential method, we study the motion of a spinning test particle on the equatorial plane of a polymer black…
Systems of pinned billiard balls serve as simplified models of collisions, where all particles remain fixed in their positions while their (pseudo-)velocities evolve in accordance with the laws of conservation of energy and momentum. For…
Gravitational billiards provide an experimentally accessible arena for testing formulations of nonlinear dynamics. We present a mathematical model that captures the essential dynamics required for describing the motion of a realistic…
In a set of experiments, Couder et. al. demonstrate that an oscillating fluid bed may propagate a bouncing droplet through the guidance of the surface waves. We present a dynamical systems model, in the form of an iterative map, for a…
We describe an experiment dedicated to the study of the trajectories of a ball bouncing randomly on a vibrating plate. The system was originally used, considering a sinusoidal vibration, to illustrate period doubling and the route to chaos.…
Swimming in curved spacetimes is a phenomenon whereby free bodies in curved spacetimes are able to propel themselves by performing cyclic internal motions. When originally proposed, it was further suggested that, in the limit of fast…
Projectile motion is a constant theme in introductory-physics courses. It is often used to illustrate the application of differential and integral calculus. While most of the problems used for this purpose, such as maximizing the range, are…
Recent experiments and numerical simulations have shown that certain types of microorganisms "reflect" off of a flat surface at a critical angle of departure, independent of the angle of incidence. The nature of the reflection may be active…
The classical and quantum behavior of a particle inside a square box under the influence of the gravitational field is studied. Detailed calculations on periodic orbits, probability densities as well as expectation values and uncertainties…
The period of oscillation of a simple pendulum ($T = 2\pi\sqrt{l/g}$) is a familiar formula to the average first-year physics student. However, deriving this expression from first principles involves solving a non-linear differential…
We experimentally investigate electrical transport properties of graphene, which is a two dimensional (2D) conductor with relativistic energy dispersion relation. By investigating single- and bi-layer graphene devices with different aspect…
In this paper the problem of estimating the number of periodical billiard trajectories is considered. The main result is the theorem on Morse theory for periodical billiard trajectories.
Have you ever played or watched a game of pool? If so, you have already seen a billiard system in action. In mathematics and physics, a billiard system describes a ball that moves in straight lines and bounces off walls. Despite these…
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…
We describe a simple numerical simulation, suitable for an undergraduate project (or graduate problem set), of the Brownian motion of a particle in a Hooke-law potential well. Understanding this physical situation is a practical necessity…
Many modern theories which try to unify gravity with the Standard Model of particle physics, as e.g. string theory, propose two key modifications to the commonly known physical theories: i) the existence of additional space dimensions; ii)…