Related papers: Pedal coordinates, Dark Kepler and other force pro…
In this paper we have resolved the apparent paradox of different mechanical equations for force and torque governing the motion of a charged particle in different inertial frames. The same paradox arises in all usual ``explanations'' of the…
While a wide variety of astrophysical and cosmological phenomena suggest the presence of Dark Matter, all evidence remains via its gravitational effect on the known matter. As such, it is conceivable that this evidence could be explained by…
Forces defined in the framework of optical reference geometry are introduced in the case of stationary and axially symmetric Kerr black-hole and naked-singularity spacetimes with a repulsive cosmological constant. Properties of the forces…
The dynamical parameters conventionally used to specify the orbit of a test particle in Kerr spacetime are the energy $E$, the axial component of the angular momentum, $L_{z}$, and Carter's constant $Q$. These parameters are obtained by…
New techniques to evaluate the clock effect using light are described. These are based on the flatness of the cylindrical surface containing the world lines of the rays constrained to move on circular trajectories about a spinning mass. The…
Kepler's laws of planetary motion are acknowledged as highly significant to the construction of universal gravitation. The present study demonstrates different ways to derive the law of equal areas for the Earth by general geometrical and…
There are known problems of Lorentz-Dirac equation for moving with acceleration charged particle in classical electrodynamics. The model of extended in one dimension particle is proposed and shown that electromagnetic self-interaction can…
It is argued that, contrary to conventional wisdom, no trustworthy universal self-force/radiative corrections to the Lorentz force equation, can be derived from the basic tenets of classical electrodynamics. This concords with the apparent…
I discuss the influence of adding the air resistance and the kinetic friction to the classical mechanics homework-problem: finding the motion of a body sliding down a hemispherical hill. For a physically realistic ($\propto v^2$) form of…
We show that it is possible to obtain self-consistent and physically acceptable relativistic classical equations of motion for a point-like spin-half particle possessing an electric charge and a magnetic dipole moment, directly from a…
The field equations of a generalized $f(R)$ type gravity model, in which there is an arbitrary coupling between matter and geometry, are obtained. The equations of motion for test particles are derived from a variational principle in the…
After some more than four centuries from the formulation and publication (in Astronomia Nova) of the Kepler's Equation, which relates the eccentric (and, intermediately, the true) anomaly of the planetary trajectories to the uniformly…
This note includes results of a study of stationary spherically symmetric ``dark holes'', objects merging central black holes and peripheral scalar graviton dark haloes arising in the framework of the modified gravity -- the quartet-metric,…
Scalar fields coupled to dark matter by conformal or disformal transformations give rise to a general class of scalar-tensor theories which leads to a rich phenomenology in a cosmological setting. While this possibility has been studied…
Electromagnetic waves with phase defects in the form of vortex lines combined with a constant magnetic field are shown to pin down cyclotron orbits (Landau orbits in the quantum mechanical setting) of charged particles at the location of…
The Stark problem is Kepler problem with an external constant acceleration. In this paper, we study the periodic orbits for Stark problem for both planar case and spatial case. We have conducted a detailed analysis of the invariant tori and…
The Kepler-Heisenberg problem is that of determining the motion of a planet around a sun in the sub-Riemannian Heisenberg group. The sub-Riemannian Hamiltonian provides the kinetic energy, and the gravitational potential is given by the…
The interaction of a charged particle with its own field results in the "self-force" on the particle, which includes but is more general than the radiation reaction force. In the vicinity of the particle in curved spacetime, one may follow…
We seek periodic trajectories of a system of multiple mutually repelling electrons on a half-line, with an attractive nucleus sitting at the origin. We adopt a variational viewpoint and study critical points of the associated…
The Classical Coordinate System is geometrical by nature with time being an external variable. Constructing a classical coordinate system employs a point-like signal with infinite speed. In Special Relativity Theory the speed is limited but…