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A non-linear non-perturbative relativistic atomic theory introduces spin in the dynamics of particle motion. The resulting energy levels of Hydrogen atom are exactly same as the Dirac theory. The theory accounts for the energy due to…
The first integrals of the Kepler problem are used to compute preliminary orbits starting from two short observed arcs of a celestial body, which may be obtained either by optical or radar observations. We write polynomial equations for…
We present a new method for computing orbits in the perturbed two-body problem: the position and velocity vectors of the propagated object in Cartesian coordinates are replaced by eight orbital elements, i.e., constants of the unperturbed…
A level orbit of a mechanical Hamiltonian system is a solution of Newton equation that is contained in a level set of the potential energy. In 2003, Mark Levi asked for a characterization of the smooth potential energy functions on the…
Using the first law of binary black-hole mechanics, we compute the binding energy E and total angular momentum J of two non-spinning compact objects moving on circular orbits with frequency Omega, at leading order beyond the test-particle…
The periodic orbit conjecture states that, on closed manifolds, the set of lengths of the orbits of a non-vanishing vector field all whose orbits are closed admits an upper bound. This conjecture is known to be false in general due to a…
We show that work done by the non conservative forces along a stable limit cycle attractor of a dissipative dynamical system is always equal to zero. Thus, mechanical energy is preserved on average along periodic orbits. This balance…
Both orbital and rotational dynamics employ the method of variation of parameters. We express, in a non-perturbed setting, the coordinates (Cartesian, in the orbital case, or Eulerian in the rotation case) via the time and six adjustable…
This study investigates the different novel forms of the dynamical equations of a particle orbiting a rotating asteroid and the effective potential, the Jacobi integral, etc. on different manifolds. Nine new forms of the dynamical equations…
Variable mass systems are a classic example of open systems in classical mechanics. The reaction forces due to mass variation propel ships, balloons, and rockets. Unlike free constant mass systems, the angular momentum of these systems is…
Earth rotation is determined by polar motion (PM) and length of day (lod). The excitation sources of PM are torques linked to fluid circulations ("geophysical excitations"), and those of lod to luni-solar tides ("astronomical excitations").…
The global rotational degrees of freedom in the Schr\"{o}dinger equation for an $N$-body system are completely separated from the internal ones. After removing the motion of center of mass, we find a complete set of $(2\ell+1)$ independent…
The importance of the energy spectrum of bound states and their restrictions in quantum mechanics due to the different methods have been used for calculating and determining the limit of them. Comparison of Schrodinger-like equation…
It is proved, using the curved line element of a spherically symmetric charged object in general relativity and the Schwinger discharge mechanism of quantum field theory, that the orbital periods $T_{\infty}$ of test particles around…
The post-post-Newtonian (2PN) accurate mass quadrupole moment, for compact binaries of arbitrary mass ratio, moving in general orbits is obtained by the multi-polar post Minkowskian approach of Blanchet, Damour, and Iyer (BDI). Using this,…
We set forth a method to analyze the orbital angular momentum of a light field. Instead of using the canonical formalism for the conjugate pair angle-angular momentum, we model this latter variable by the superposition of two independent…
In this work, we perform a detailed analysis of the equatorial motion of the charged test particles in Kerr-Newman-Taub-NUT spacetime. By working out the orbit equation in the radial direction, we examine possible orbit types. We…
In the present work, we study the classical behavior of an electric dipole in presence of an external uniform magnetic field. We derive equations and constants of motion from the Lagrangian formulation. We obtain an infinitely periodic…
Within the framework of Bonnor's exact solution describing a massive magnetic dipole, we study the motion of neutral and electrically charged test particles. In dependence on the Bonnor spacetime parameters, we determine regions enabling…
Near a black hole or an ultracompact star, motion of particles is governed by strong gravitational field. Electrically charged particles feel also electromagnetic force arising due to currents inside the star or plasma circling around. We…