Related papers: Ballistic trajectory: parabola, ellipse, or what?
In this paper we create a model of particle motion on a three-dimensional lattice using discrete random walk with small steps. We rigorously construct a probability space of the particle trajectories. Unlike deterministic approach in…
In general relativity the gravitational field is a manifestation of spacetime curvature and unlike the electromagnetic field is not a force field. A particle falling in a gravitational field is represented by a geodesic worldline which…
This paper studies the quantum dynamics of a charged particle in a 2D square lattice, under the influence of electric and magnetic fields, the former being aligned with one of the lattice axes and the latter perpendicular to the lattice…
Vortices play an unique role in heat and momentum transports in astro- and geo-physics, and it is also the origin of the Earth's dynamo. A question existing for a long time is whether the movement of vortices can be predicted or understood…
Different sequences of ellipsoids are represented on the ellipticity-rotation plane. The rotation parameter is defined as the ratio of kinetic energy related to the mean tangential equatorial velocity component to kinetic energy related to…
Along with weaving together observations, experiments, and theoretical constructs into a coherent mesh of understanding of the world around us, physics over its past five centuries has continuously refined the base concepts on which the…
Despite the importance of non-equilibrium statistical mechanics in modern physics and related fields, the topic is often omitted from undergraduate and core-graduate curricula. Key aspects of non-equilibrium physics, however, can be…
The restricted planar elliptic three body problem (RPETBP) describes the motion of a massless particle (a comet) under the gravitational field of two massive bodies (the primaries, say the Sun and Jupiter) revolving around their center of…
Beyond the Newtonian approximation, gravitational fields in general relativity can be described using a formalism known as gravitoelectromagnetism. In this formalism a vector potential, the gravitomagnetic potential, arises as a result of…
We investigate the motion of an inert (massive) particle being impinged from below by a particle performing (reflected) Brownian motion. The velocity of the inert particle increases in proportion to the local time of collisions and…
In this paper we consider satellite trajectories in central force field with quadratic drag using two formalisms. The first using polar coordinates in which the angular momentum plays a dominant role. The second is in Levi-Civita…
We investigate the suitability of natural orbitals as a basis for describing many-body excitations. We analyze to which extend the natural orbitals describe both bound as well as ionized excited states and show that depending on the…
In previous studies the dynamics of the relativistic particle moving along the rotating pipe was investigated. The simple gedanken experiment was considered. It was shown that at large enough velocities a centrifugal force acting on the…
The notion of microscopic state of the system at a given moment of time as a point in the phase space as well as a notion of trajectory is widely used in classical mechanics. However, it does not have an immediate physical meaning, since…
The trajectory of a spherical object which falls freely in a gravitational field is fixed by its initial position and velocity. However, an object which can control its shape can also control its motion: Except where forbidden by symmetries…
An approach to modelling the universe based on the requisites of gravitational energy. This model is explained as it relates to the stages of the universal life cycle and the continued existence of the universe as it is known today. The…
We explore the gravitational dynamics of falling through planetary interiors. Two trajectory classes are considered: a straight cord between two surface points, and the brachistochrone path that minimizes the falling time between two…
A generalization of General Relativity is studied. The standard Einstein-Hilbert action is considered in the Palatini formalism, where the connection and the metric are independent variables, and the connection is not symmetric. As a result…
In Minkowski spacetime, we consider an isolated system made of two pointlike bodies interacting at a distance, in the nonradiative approximation. Our framework is the covariant and a priori Hamiltonian formalism of "predictive relativistic…
The two equations of motion for a test particle are compared with each other. One is in the Non commutative space involving a static rigid sphere (as a source of central force) and the other is in the usual space involving a slowly…