Related papers: A mechanical model that exhibits a gravitational c…
We analyze the frictionless motion of a point-like particle that slides under gravity on an inverted conical surface. This motion is studied for arbitrary initial conditions and a general relation, valid within 13%, between the periods of…
Concept of curvature of liquid surrounding a spherical surface seems obvious in daily life, but based on earthly conditions everywhere. However, our understanding about the concept seems more transparent when we keep the system out of the…
A simple geometrical model is presented for the gravity-driven motion of a single particle on a rough inclined surface. Adopting a simple restitution law for the collisions between the particle and the surface, we arrive at a model in which…
The motion of a classical spinning test particle in the field of a weak plane gravitational wave is studied. It is found that the characteristic dimensions of the particle's orbit is sensitive to the ratio of the spin to the mass of the…
A wheel or sphere rolling without slipping on the inside of a sphere in a uniform gravitational field can have stable circular orbits that lie wholly above the "equator", while a particle sliding freely cannot.
In rotations with a binary symbolic dynamics, a critical curve is the locus of parameters for which the boundaries of the partition that defines the symbolic dynamics are connected via a prescribed number of iterations and symbolic…
We find that circular kinks form on the surface of granular material when the axis of rotation is tilted more than the angle of internal friction of the material. Radius of the kinks is measured as a function of the spinning speed and the…
A model of the gravitational dipole is proposed in a close analogy to that of the global monopole. The physical properties and the range of validity of the model are examined as is the motion of test particles in the dipole background. It…
When granular systems are modeled by frictionless hard spheres, particle-particle collisions are considered as instantaneous events. This implies that while the velocities change according to the collision rule, the positions of the…
The nature of boundedness of orbits of a particle moving in a central force field is investigated. General conditions for circular orbits and their stability are discussed. In a bounded central field orbit, a particle moves clockwise or…
The motion of a block slipping on a surface is a well studied problem for flat and circular surfaces, but the necessary conditions for the block to leave (or not) the surface deserve a detailed treatment. In this article, using basic…
We describe the dynamics of a stream of equally spaced macroscopic particles in orbit around a central body (e.g. a planet or star). A co-orbital configuration of small bodies may be subject to gravitational instability, which takes the…
Non-relativistic particles that are effectively confined to two dimensions can in general move on curved surfaces, allowing dynamical phenomena beyond what can be described with scalar potentials or even vector gauge fields. Here we…
It is often assumed that a warped galaxy can be modeled by a set of rings. This paper verifies numerically the validity of this assumption by the study of periodic orbits populating a heavy self-gravitating warped disk. The phase space…
Dynamics of regular clusters of many non-touching particles falling under gravity in a viscous fluid at low Reynolds number are analysed within the point-particle model. Evolution of two families of particle configurations is determined: 2…
We present a model for the motion of hard spherical particles on a two dimensional surface. The model includes both the interaction between the particles via collisions, as well as the interaction of the particles with the substrate. We…
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…
A stationary rotating surface is a compact surface in Euclidean space whose mean curvature $H$ at each point $x$ satisfies $2H(x)=a r^2+b$, where $r$ is the distance from $x$ to a fixed straight-line $L$, and $a$ and $b$ are constants.…
We extend the model of surface granular flow proposed in \cite{bcre} to account for the effect of an external `wind', which acts as to dislodge particles from the static bed, such that a stationary state of flowing grains is reached. We…
The radius of the circular orbit for the time-like or light-like test particle in a background of general spherically symmetric spacetime is viewed as a characterized quantity for the thermodynamic phase transition of the corresponding…