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.     

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.     

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 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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

Parametric dependence of the collinear equilibria and of their stability in the equatorial magnetic-binary problem

A magnetic-binary system is completely determined by means of eight parameters. Their variation affects directly the qualitative characteristics of the system. In this paper we investigate numerically the parametric dependence of the collinear equilibria in the equatorial magnetic-binary problem. Their stability is also examined employing the classical method of the characteristic roots associated with each equilibrium point. The whole research is documented by diagrams and tables containing the obtained results.     

A fully automated data reduction pipeline for the FRODOSpec integral field spectrograph

A fully autonomous data reduction pipeline has been developed for FRODOSpec, an optical fibre‐fed integral field spectrograph currently in use at the Liverpool Telescope. This paper details the process required for the reduction of data taken using an integral field spectrograph and presents an overview of the computational methods implemented to create the pipeline. Analysis of errors and possible future enhancements are also discussed (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A Cauchy problem for Milne's integral equation with a pincherle-goursat kernel

In a series of our preceding papers (cf. Bellman and Ueno, 1971a, 1971b, 1972a, 1972b, 1972c; Ueno 1972), with the aid of invariant imbedding technique, we transformed the two point boundary value problem for integral equations into the initial-value problem. In this paper, extending the procedure to the Milne's integral equation, whose kernel is expanded into a double Fourier cosine series, we show how to find a Cauchy system for the required solution of Milne's integral equation and the Fredholm resolvent. The obtained integro-differential equations are reduced to large system of ordinary differential equations with known initial conditions. Then, they are suitable for the numerical computation of the solution by the modern high-speed computer.     

On the energy integral for first post-Newtonian approximation

The post-Newtonian approximation for general relativity is widely adopted by the geodesy and astronomy communities. It has been successfully exploited for the inclusion of relativistic effects in practically all geodetic applications and techniques such as satellite/lunar laser ranging and very long baseline interferometry. Presently, the levels of accuracy required in geodetic techniques require that reference frames, planetary and satellite orbits and signal propagation be treated within the post-Newtonian regime. For arbitrary scalar W and vector gravitational potentials \(W^j (j=1,2,3)\), we present a novel derivation of the energy associated with a test particle in the post-Newtonian regime. The integral so obtained appears not to have been given previously in the literature and is deduced through algebraic manipulation on seeking a Jacobi-like integral associated with the standard post-Newtonian equations of motion. The new integral is independently verified through a variational formulation using the post-Newtonian metric components and is subsequently verified by numerical integration of the post-Newtonian equations of motion.     

The second integral of the restricted problem in regularized elements

A perturbation series integral for the restricted problem of three bodies is derived by use of a new set of canonical elements for the regularized two-body problem. These elements are similar to theKS elements of Stiefel and Scheifele, but they contain small parameters other than the semimajor axis. The variable analogous to the longitude of perihelion not only remains well defined as the orbit approaches a circle, but also it can be used as a second small parameter. Regularized elements permit canonical use of the eccentric anomaly as independent variable, but most of the major benefits of regularization in the two-body problem do not carry over to perturbation theory.