Related papers: The comfortable roller coaster -- on the shape of …
Study of the classical motion of two identical particles on a plane subject to non-Coulomb potentials in a constant magnetic field presented in polar coordinates. With the rigorous analysis of the potentials and the constants of motion, we…
We examine the motion of a relativistic charged particle in a constant magnetic field perturbed by gravitational waves incident along the direction of the magnetic field. We apply a generalized energy conservation law to compute the…
We consider a run an tumble particle with two velocity states $\pm v_0$, in an inhomogeneous force field $f(x)$ in one dimension. We obtain exact formulae for its velocity $V_L$ and diffusion constant $D_L$ for arbitrary periodic $f(x)$ of…
When a falling ball chain strikes a surface, a tension is created that pulls the chain downward. This causes a downward acceleration that is larger than free-fall, which has been observed by recent experiments. Here a theoretical…
In the merry-go-round fictitious forces are acting like centrifugal force and Coriolis force. Like the Lorentz force Coriolis force is velocity dependent and, following Arnold, can be modeled by twisting the symplectic form. If the…
We investigate the motion of a hard cylinder rolling down a soft inclined plane. The cylinder is subjected to a viscous drag force and stochastic fluctuations due to the surrounding medium. In a wide range of parameters we observe…
We investigate the motion of one and two charged non-relativistic particles on a sphere in the presence of a magnetic field of uniform strength. For one particle, the motion is always circular, and determined by a simple relation between…
We investigate regular configurations of a small number of particles settling under gravity in a viscous fluid. The particles do not touch each other and can move relative to each other. The dynamics is analyzed in the point-particle…
Given a real vector space V of finite dimension, together with a particular homogeneous field of bivectors that we call a "field of projective forces", we define a law of dynamics such that the position of the particle is a "ray" i.e. a…
Even professional baseball players occasionally find it difficult to gracefully approach seemingly routine pop-ups. This paper describes a set of towering pop-ups with trajectories that exhibit cusps and loops near the apex. For a normal…
We investigate classical scattering off a harmonically oscillating target in two spatial dimensions. The shape of the scatterer is assumed to have a boundary which is locally convex at any point and does not support the presence of any…
We study the dynamics of vortices formed in a superfluid film adsorbed on the curved two-dimensional surface of a cone. To this aim, we observe that a cone can be unrolled to a sector on a plane with periodic boundary conditions on the…
We investigate the problem of determining the shape of a rotating celestial object - e.g., a comet or an asteroid - under its own gravitational field. More specifically, we consider an object symmetric with respect to one axis - such as a…
The scalar and vector potentials of the acceleration field and the pressure field are calculated for the first time for a rotating relativistic uniform system, and the dependence of the potentials on the angular velocity is found. These…
It is commonly observed that objects in a gravitational field experience a rate of acceleration that is independent of their mass and that, as a result, all massive objects with the same initial conditions follow the same trajectory. It is…
Laboratory experiments on gravitation are usually performed with objects of constant density, so that the analysis of the forces concerns only the geometry of their shape. In an ideal experiment, the shapes of the constituent parts will be…
For a Chaplygin sleigh moving in the presence of weak friction, we present and investigate two mechanisms of arising acceleration due to oscillations of an internal mass. In certain parameter regions, the mechanism induced by small…
It was shown that pedal coordinates provides natural framework in which to study force problems of classical mechanics in the plane. A trajectory of a test particle under the influence of central and Lorentz-like forces can be translated…
We prove the existence of some types of periodic orbits for a particle moving in Euclidean three-space under the influence of the gravitational force induced by a fixed homogeneous circle. These types include periodic orbits very far and…
Studies of particle motion in vortical flows have mainly focused on point-like particles, either inertial or self-propelled. This approximation assumes that the velocity field that surrounds the particle is linear. We consider an…