Planar motions of a charged particle in a magnetic-binary system with spherical or oblate primaries

In this paper we present for the first time simple symmetric motions in the planar magnetic-binary problem where both primaries are spherical bodies or oblate spheroids. From the study of this case it follows that there is a dense and complicated distribution of the families of such motions in the phase space. Our results also show that the orbital characteristics of the particle and the configuration of the phase space are appreciably affected by the oblateness of the primaries only if these parameters become sufficiently large.     

The rotating magnetic-binary problem: A new realistic description of magnetic-binary systems

The authors generalize the magnetic-binary problem by introducing the individual rotation of the magnetic moments of the two bodies about their respective origins. In this part of the project they give only the Lagrange and Hamilton form of the equations of motion and comment on the time dependence of the orientation of these moments. Based on this formulation they suggest a new model of the Earth-Sun system, which they hope will help the investigation of the real particle's behaviour within this system.     

The areas of motion in the planar magnetic-binaries problem

The purpose of this article is to present the areas of motion in the planar magneticbinaries problem and show their contribution to the behavioral study of a charged particle moving in such a system.     

The equatorial equilibrium-configurations of the magnetic-binary problem

The equilibrium-configurations of the Magnetic-Binary problem are investigated in the case of equatorial motion. The law of this constrained motion is derived and then the procedure for localizing the equilibrium points is developed. The type of equilibrium is also studied by means of the known method of variational equations.     

The symplectic character of the three-dimensional magnetic-binary problem

The scale-covariant theory of gravitation, which was proposed by Canutoet al. (1977), assumes that gravitational and atomic units are related by a scalar function of space-time. The cosmology based on this theory can explain very well the 3K radiation, as well as Hubble's redshift law. However, Falik (1979) derived a result from the scale-covariant cosmology which was in conflict with the observed helium abundance. Contrary to Falik, we show in this paper that if we choose a gauge functionβ～t ^α and α satisfies the condition ?1/3<α<1, the scale-covariant cosmology will be consistent with the observed cosmic-helium abundance. The value α=1/2 has recently been suggested by Canuto and Goldman (1982) on general grounds.     

Equilibrium points in the planar magnetic-binary problem

This article deals with the analytical investigation of the number and location of equilibrium points, in the planar magnetic-binary problem, by taking into consideration the influence of the parameters which exactly determine the model of such a system.     

The existence of three-dimensional symmetric orbits in the magnetic-binary problem

We study the existence of three-dimensional symmetric orbits in a magnetic-binary system. We point out that only two kinds of such orbits exist, depending on the orientation of both magnetic momentsM _i,i=1, 2; one with respect to the plane,y=0 and one with respect to thex-axis of the rotating-coordinate system.     

Regularization of the equatorial magnetic-binary problem

The differential equations which describe the equatorial motion of a particle in a magnetic-binary system are regularized by a transformation of the dependent and independent variables. The new equations of motion, which are simpler than the original ones, with only linear velocity and acceleration terms occurring, show the invariant form of the law of motion. Finally, the distinction between the zero-velocity curves and the isotachs in the transformed space is also discussed.     

On Goudas' surfaces in the magnetic-binary problem

The containment property Goudas' surfaces has been studied in this paper. Physical implications of this property a consequently discussed. A general relationship is obtained, which connects the sizes of those surfaces, the magnetic moments of two stars and their mean motion.     

Areas of equatorial motion in the magnetic-binary problem

In the process of modelling the Magnetic-Binary systems, we deal with the permissible areas of motion in the equatorial planes of the representative model. The zero velocity curves, derived by the well known steepest descent method, provide the means for determining these areas. Further these curves reveal all the equilibrium points located on the above planes.     

Application of high-order Runge-Kutta methods in the magnetic-binary problem

Our intention in this paper is to present the results obtained from a systematic comparative study of several high-order Runge-Kutta methods as applied in a composite problem of celestial dynamics, namely the magnetic-binary problem.     

Three-dimensional equilibria and their stability in the magnetic-binary problem

The author's aim has been to study the three-dimensional equilibrium points of a magnetic-binary system. First he develops the procedure for finding these equilibria, and then he studies their stability by using the method of the characteristic exponents. Finally an example in a concrete system is given to verify the described procedure.     

A comparison of numerical integration methods in the equatorial magnetic-binary problem

In this paper we compare several Runge-Kutta type methods of fourth-order when they are applied in the Equatorial Magnetic-Binary Problem (EMBP) for which the analytical solutions are not known. The results of the comparison are presented with tables and diagrams, and the most efficient method is proposed according to the used criteria which are described.Section of Mechanics.Section of Mathematics.     

The charged particle in the magnetosphere of a rotating neutron star

The motion of charged particles in a pulsar magnetosphere is examined in the present paper. Using the non-relativistic approximation, the trajectories of the charged particles are investigated qualitativley both in the case of axial and in the case of incline rotator. The obtained results can be used for the construction of the pulsar magnetosphere.     

New families of simple symmetric motions in the equatorial magnetic-binary problem

In this paper we present 14 new families of simple symmetric motions in the equatorial magnetic-binary problem. The study of the families found so far lead to some interesting remarks which although they are referred to a certain kind of motion, they can, however, characterize the totality of the solutions provided that the hypothesis of Poincaré (1892) holds in this case.     

Motion of a charged particle around a black hole permeated by magnetic field and its chaotic characters

Motion of a charged particle around a black hole immersed in magnetic field is calculated. It is shown that this motion has a chaotic property depending on initial parameters.     

The periodicity of a charged particle motion in a magnetic dipole field

The author's purpose is to present in this article the evidence of his intuition on the periodic behavior of a charged particle, moving in a magnetic dipole field, that is achieved by adopting the Alfvén's analysis of the motion into the composite of two motions and studying the contribution of these motions into the general behavior of the charged particle, separately.     

A reduction of the magnetic-binary problem by means of the energy integral

The author's aim in this article has been to present the magnetic-binary problem in a new form different from the usual, by using a process of reduction of a dynamical problem to another one with fewer degrees of freedom.