相关论文: The monotonicity of the apsidal angle in power-law…
In a central force system the angle between two successive passages of a body through pericenters is called the apsidal angle. In this paper we prove that for central forces of the form $f(r)\sim \lambda r^{-(\alpha+1)}$ with $\alpha<2$ the…
This paper concerns the behaviour of the apsidal angle for orbits of central force system with homogenous potential of degree $-2\leq \alpha\leq 1$ and logarithmic potential. We derive a formula for the apsidal angle as a fixed-end points…
We derive an expression for the determination of the apsidal angles that holds good for arbitrary central potentials. Then we discuss under what conditions the apsidal angles remain independent of the mechanical energy and angular momentum…
A method is proposed for the determination of the position and inclination angles of the plane of a spiral galaxy based on the assumption that every spiral arm is a monotonic function of the radius versus azimuthal angle. This method may…
We study the phenomenon of gyroscopic precession and the analogues of inertial forces within the framework of general relativity. Covariant connections between the two are established for circular orbits in stationary spacetimes with axial…
We present an application of a recently introduced variant of orbit space reduction for symmetric dynamical systems. This variant works with suitable localizations of the algebra of polynomial invariants of the group actions, and provides…
Introducing a radially dependent magnetic field into Newton's off-center circular orbits potential so as to preserve the $E=0$ dynamical symmetry leads to a unique choice of field that can be identified as the inclusion of a magnetic…
The nature of boundedness of orbits of a particle moving in a central force field is investigated. General conditions for circular orbits and their stability are discussed. In a bounded central field orbit, a particle moves clockwise or…
We extend our previous work on the evolution of close binary systems with misaligned orbital and spin angular momenta resulting from non-dissipative tidal interaction to include all physical effects contributing to apsidal motion. In…
We hereby study the stability of a massless probe orbiting around an oblate central body (planet or planetary satellite) perturbed by a third body, assumed to lie in the equatorial plane (Sun or Jupiter for example) using an Hamiltonian…
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…
In Book 1, Proposition 7, Problem 2 of his 1687 Philosophiae Naturalis Principia Mathematica, Isaac Newton poses and answers the following question: Let the orbit of a particle moving in a central force field be an off-center circle. How…
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…
While studying the motion of a heavy symmetric top, in general, constants of motion are used. Some students may want to understand the motion in terms of torque, which can lie on their routine based on the usage of Newton's second law.…
We study the influence of perturbations in the three dimensional isotropic harmonic oscillator problem considering different perturbing force laws and apply our results in the context of celestial mechanics, particularly in the movement of…
The dynamo instability is investigated in the limit of infinite magnetic Prandtl number. In this limit the fluid is assumed to be very viscous so that the inertial terms can be neglected and the flow is slaved to the forcing. The forcing…
In the paper we consider systems in oscillating force fields such that the classical method of averaging can be applied. We present sufficient conditions for the existence of forced oscillations in such systems and study the asymptotic…
Considering the definition of inertial forces acting on a test particle, following non-circular geodesics, in static and stationary space times we show that the centrifugal force reversal occurs only in the case of particles following…
The calculus of apsidal precession frequencies of the planets is developed by means of a perturbation thecnique. A model of concentric rings (ring model), suitable for improving calculations, is introduced. Conclusive remarks concerning a…
The N\'eel order of an antiferromagnet subject to a spin torque can undergo precession in a circular orbit about any chosen axis. To orient and stabilize the motion against the effects of magnetic anisotropy, the spin polarization should…