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The orbits about Lagrangian equilibrium points are important for scientific investigations. Since, a number of space missions have been completed and some are being proposed by various space agencies. In light of this, we consider a more…
A nonrelativistic particle released from rest at the edge of a ball of uniform charge density or mass density oscillates with simple harmonic motion. We consider the relativistic generalizations of these situations where the particle can…
Rotating relativistic stars are receiving significant attention in recent years, because of the information they can yield about the equation of state of matter at extremely high densities and because they are one of the more possible…
We study radial perturbations of a wormhole in $R^2$ gravity to determine regions of stability. We also investigate massive and massless particle orbits and tidal forces in this space-time for a radially infalling observer.
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…
In order to simulate rigidly rotating polytropes we have simulated systems of $N$ point particles, with $N$ up to 1800. Two particles at a distance $r$ interact by an attractive potential $-1/r$ and a repulsive potential $1/r^2$. The…
A Hamiltonian formalism is employed to elucidate the effects of the Stern-Gerlach force on beams of relativistic spin-polarized particles, for passage through a localized region with a static magnetic or electric field gradient. The problem…
We consider the system of Maxwell equations and Lorentz torque equation which describes a motion of charge in electromagnetic field. Under certain symmetry conditions on charge distribution and on initial fields the mass center of the…
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…
The single particle stability in a circular accelerator is of concern especially for operational regimes involving beam storage of hours. In the proximity to a resonance this stability domain shrinks, and the phase space fragments into a…
Rotating relativistic stars have been studied extensively in recent years, both theoretically and observationally, because of the information one could obtain about the equation of state of matter at extremely high densities and because…
A general study of the stability of equatorial circular orbits in static axially symmetric gravitating systems is presented. Important circular geodesics as the marginally stable orbit, the marginally bounded orbit and the photon orbit are…
The effect of the relativistic spin rotation on two--particle spin states, conditioned by the setting of the spins of the particles in their rest frames and by the noncommutativity of the Lorentz transformations along noncolinear…
We consider the motion of a spinning relativistic particle in external electromagnetic and gravitational fields, to first order in the external field, but to an arbitrary order in spin. The correct account for the spin influence on the…
A discrete and exact algorithm for obtaining planetary systems is derived in a recent article (Eur. Phys. J. Plus 2022, 137:99). Here the algorithm is used to obtain planetary systems with forces different from the Newtonian inverse square…
We investigate the motion of a magnetized particle orbiting around a black hole in braneworld placed in asymptotically uniform magnetic field. The influence of brane parameter on effective potential of the radial motion of magnetized…
We consider the systematic force on a heavy probe induced by interaction with an overdamped diffusive medium where particles undergo a rotating force around a fixed center. The stiffness matrix summarizes the stability of the probe around…
Orbits in the principal planes of triaxial potentials are known to be prone to unstable motion normal to those planes, so that three dimensional investigations of those orbits are needed even though they are two dimensional. We present here…
We discuss constants of motion of a particle under an external field in a curved spacetime, taking into account the Hamiltonian constraint which arises from reparametrization invariance of the particle orbit. As the necessary and sufficient…
The motion of test particles along circular orbits in the vacuum $C$ metric is studied in the Frenet-Serret formalism. Special orbits and corresponding intrinsically defined geometrically relevant properties are selectively studied.