[en] 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. (orig.)

[en] A cluster expansion for the bound state of nuclei is proposed. In such expansion the nucleus is considered as composed of N distinguishable clusters interacting with each other by pairwise potentials (C.P.)

[en] Outgoing asymptotic orbits at a collinear equilibrium point of the elliptic restricted three-body problem are constructed analytically and numerically, and those which intersect perpendicularly the axis of symmetry are selected by means of a numerical procedure of differential corrections. Due to the symmetry properties of the problem, the latter orbits terminate asymptotically back to the equilibrium point, and therefore provide a kind of 'asymptotic trapping' at the unstable equilibrium; a trapping mechanism based on 'long duration of passage' rather than stability of motion. (Auth.)

[en] The aim of this paper is the detection of three-dimensional asymmetric periodic orbits. An iterative procedure is described for the determination of the bifurcations of families of plane asymmetric periodic solutions of the restricted three-body problem with such of three-dimensional ones. It is applied to the two previously established bifurcations of this type. For each of them a 'bifurcation series' is obtained covering the entire range of the mass parameter of the problem. The stability of these bifurcation orbits is examined and it is found that in each case there are two subintervals of the range of the mass parameter for which these orbits are stable, one of them containing cases of astronomical interest. Typical three-dimensional asymmetric periodic orbits of the bifurcating families are also given. (author)

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[en] Saari’s homographic conjecture in an N-body problem under the Newton gravity is as follows. Configurational measure $\mathrm{\mu <!--\; ??\; -->}=\sqrt{I}U$, which is the product of the square root of the moment of inertia I = (∑m_k)⁻¹∑m_im_jr²_ij and the potential function U = ∑m_im_j/r_ij, is constant if and only if the motion is homographic. Where m_k represents the mass of the body k and r_ij represents the distance between bodies i and j. We prove this conjecture for the planar equal-mass three-body problem. In this work, we use three sets of shape variables. In the first step, we use ζ = 3q₃/(2(q₂ − q₁)), where $q_k\in <!--\; ???\; -->\mathbb{C}$ represents the position of the body k. Using r₁ = r₂₃/r₁₂ and r₂ = r₃₁/r₁₂ in the intermediate step, we finally use μ itself and ρ = I^3/2/(r₁₂r₂₃r₃₁). The shape variables μ and ρ make our proof simple. (paper)

[en] The use of spherical functions in dynamical problems is very common. As a rule, they arise in perturbing functions. It is well known that passing from one reference frame to another is accompanied by a double transformation of the perturbation function. That is why problems lose their simplicity and elegance. The problem of two solid bodies is a typical example in this respect. In the present paper the questions connected with the transformation of the spherical functions when passing from one reference frame to another frame are considered. Traditional functions are generally unsuitable as they introduce a series of difficulties in the problems. That is why complex spherical functions are used. The transformation of spherical functions due to rotation of the coordinate frame is made by means of the Wigner's functions. When translating the frame the Clebsch-Gordon's coefficients are used. (Auth.)

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