Related papers: Simple models of bouncing ball dynamics and their …
We study the collision between the cue and the ball in the game of billiards. After studying the collision process in detail, we write the (rotational) velocities of the ball and the cue after the collision. We also find the squirt angle of…
In this paper we consider cases of existence of invariant measure, additional first integrals, and Poisson structure in a problem of rigid body's rolling without sliding on plane and sphere. The problem of rigid body's motion on plane was…
A massive particle under the influence of a constant gravitational force that is bouncing inside an ideal reflecting mirror described by some function $f(x)$ is considered. For the associated flight trajectories we derive the parametric…
A single frictional elastic disk, supported against gravity by two others, rotates steadily when the supports are vibrated and the system is tilted with respect to gravity. Rotation is here studied using Molecular Dynamics Simulations, and…
In this paper, we continue discussing Q-balls in the Wick--Cutkosky model. Despite Q-balls in this model are composed of two scalar fields, they turn out to be very useful and illustrative for examining various important properties of…
Collisions of non-topological solitons, Q-balls, are studied in a typical potential in the Minimal Supersymmetric Standard Model where supersymmetry has been broken by a gravitationally coupled hidden sector. Q-ball collisions are studied…
We explore the dynamical behaviour of cosmological models involving a scalar field (with an exponential potential and a canonical kinetic term) and a matter fluid with spatial curvature included in the equations of motion. Using…
The calculation of scalar gravitational and matter perturbations during multiple-field inflation valid to first order in slow roll is discussed. These fields may be the coordinates of a non-trivial field manifold and hence have non-minimal…
The Fourier-based analysis customarily employed to analyze the dynamics of a simple pendulum is here revisited to propose an elementary iterative scheme aimed at generating a sequence of analytical approximants of the exact law of motion.…
We examine the kinetics of a snowball that is gaining mass while is rolling downhill. This dynamical system combines rotational effects with effects involving the variation of mass. In order to understand the consequences of both effects we…
Consider briefly the equations of fluid dynamics-they describe the enormous wealth of detail in all the interacting physical elements of a fluid flow-whereas in applications we want to deal with a description of just that which is…
The classical dynamics of the isotropic two-dimensional harmonic oscillator confined by an elliptic hard wall is discussed. The interplay between the harmonic potential with circular symmetry and the boundary with elliptical symmetry does…
This paper explores two instances where dissipation plays a crucial role in curbing the unbounded energy growth of particles in time-dependent billiards. The first example involves an elliptical-like billiard with inelastic collisions…
The connection between domain relaxations at individual scales and the collective heterogeneous response in non-equilibrium systems is a topic of profound interest in recent times. In a model sys- tem of constantly driven oppositely charged…
We discuss a classical nonlinear oscillator, which is proved to be a superintegrable system for which the bounded motions are quasiperiodic oscillations and the unbounded (scattering) motions are represented by hyperbolic functions. This…
We study the classical motion in bidimensional polygonal billiards on the sphere. In particular we investigate the dynamics in tiling and generic rational and irrational equilateral triangles. Unlike the plane or the negative curvature…
In this paper, two models of interest for Celestial Mechanics are presented and analysed, using both analytic and numerical techniques, from the point of view of the possible presence of regular and/or chaotic motion, as well as the…
Astute variations in the geometry of mathematical billiard tables have been and continue to be a source of understanding their wide range of dynamical behaviors, from regular to chaotic. Viewing standard specular billiards in the broader…
A quasielastic model of gravitation is developed. Gravitational field is modeled by the flow of the transient point dilatation, which is supposed to be continually emitted by a discontinuity of the turbulent fluid. Gravitational attraction…
A classic problem of the motion of a projectile thrown at an angle to the horizon in a medium with a quadratic resistance law is studied. An approximate analytical solution of the equations of projectile motion is presented, which has a…