Related papers: Elementary derivation of the Lense-Thirring preces…

A new strategy in deriving the Lense-Thirring effect, in the weak field and slow motion approximation of general relativity, on the orbital elements of a test body in the field of different central rotating sources exhibiting axial symmetry…

We calculate the precession of Keplerian orbits under the influence of arbitrary central-force perturbations. Our result is in the form of a one-dimensional integral that is straightforward to evaluate numerically. We demonstrate the…

We consider a motion of a weakly relativistic charged particle with an arbitrary spin in central potential $e/r$ in terms of classical mechanics. We show that the spin-orbital interaction causes the precession of the plane of orbit around…

It is known that a relative translational motion between the deflector and the observer affects gravitational lensing. In this paper, a lens equation is obtained to describe such effects on actual lensing observables. Results can be easily…

We review the derivation of the metric for a spinning body of any shape and composition using linearized general relativity theory, and also obtain the same metric using a transformation argument. The latter derivation makes it clear that…

We analyze the angular momentum balance for a particle undergoing Thomas precession. The relationships among relativistic torque, the center of mass, and the center of inertia for a spinning particle are clarified. We show that spin…

A covariant algorithm for deriving the conserved quantities for natural Hamiltonian systems is combined with the non-relativistic framework of Eisenhart, and of Duval, in which the classical trajectories arise as geodesics in a higher…

For the undamped Kepler potential the lack of precession has historically been understood in terms of the Runge-Lenz symmetry. For the damped Kepler problem this result may be understood in terms of the generalization of Poisson structure…

The Hamilton-Jacobi equation of classical mechanics is approached as a model reduction of conservative particle mechanics where the velocity degrees-of-freedom are eliminated. This viewpoint allows an extension of the association of the…

The vertical (Lense-Thirring) precession of the innermost accretion flows has been discussed as a sensitive indicator of the rotational properties of neutron stars (NSs) and their equation of state because it vanishes for a non-rotating…

The Lorentz transformation is entirely derived from length contraction, itself established through the known light-clock thought experiment . This makes the derivation accessible to beginning students once Eintein's two postulates have been…

We determine the nonlinear transformations between coordinate systems which are mutually in a constant symmetrical accelerated motion. The maximal acceleration limit follows from the kinematical origin and it is an analogue of the maximal…

Vectorial analysis relating to derivation of deflection of light is presented. Curvilinear acceleration is distinguished from the Newtonian polar conic acceleration. The difference between the two is due to the curvature term. Lorentz…

The relativistic precession can be quickly inferred from the nonlinear polar orbit equation without actually solving it.

The inverse square force law admits a conserved vector that lies in the plane of motion. This vector has been associated with the names of Laplace, Runge, and Lenz, among others. Many workers have explored aspects of the symmetry and…

We generalize the derivation of electromagnetic fields of a charged particle moving with a constant acceleration [1] to a variable acceleration (piecewise constants) over a small finite time interval using Coulomb's law, relativistic…

Einstein's perihelion advance formula can be given a geometric interpretation in terms of the curvature of the ellipse. The formula can be obtained by splitting the constant term of an auxiliary polar equation for an elliptical orbit into…

Kepler's first law states that the orbit of a point mass with negative energy in a classical gravitational potential is an ellipse with one of its foci at the gravitational center. In numerical simulations of this system one often observes…

In most text books of mechanics, Newton's laws or Hamilton's equations of motion are first written down and then solved based on initial conditions to determine the constants of the motions and to describe the trajectories of the particles.…

Kepler's orbits with corrections due to Special Relativity are explored using the Lagrangian formalism. A very simple model includes only relativistic kinetic energy by defining a Lagrangian that is consistent with both the relativistic…