Three-body problem, planar

The Arnold model with ft = 0 corresponds to scattering processes. In the planar Coulomb three-body problem, the asymptotic limit where one of the three bodies goes to infinity corresponds to the Arnold model with 0 = 0 [35]. For three-body clusters interacting with van der Waals potential, the Arnold model with 0 = 0 also arises when one of the three bodies goes to infinity [37]. 

Bozis G. (1976). Zero velocity surfaces for the general planar three-body problem. 

The regularization of the planar, circular, restricted three-body problem... 

Abstract In order to describe the motion of two weakly interacting satellites of a central body we suggest to use orbital elements based on the the linear theory of Kepler motion in Levi-Civita s regularizing coordinates. The basic model is the planar three-body problem with two small masses, a model in which both regular (e.g. quasi-periodic) as well as chaotic motion can occur. 

Beauge, C. (1996), On a global expansion of the disturbing function in the planar elliptic three-body problem. Cel. Mech. Dynam,. Astron. 64, 313-349. 

For this reason, we will restrict our subsequent approach to planar configurations of the two electrons and of the nucleus, with the polarization axis within this plane. This presents the most accurate quantum treatment of the driven three body Coulomb problem to date, valid in the entire nonrelativistic parameter range, without any adjustable parameter, and with no further approximation beyond the confinement of the accessible configuration space to two dimensions. Whilst this latter approximation certainly does restrict the generality of our model, semiclassical scaling arguments suggest that the unperturbed three... 

Message, P.J. (1982a) Some aspects of motion in the general planar problem of three bodies in particular in the vicinity of periodic solutions associated with near small-integer commensurabilities of orbital period. In Szebehely, V. editor, Applications of Modem Dynamics to Celestial Mechanics and Astrodynamics (The Proceedings of the N.A.T.O. Advanced Study Institute, in Istituto Antonelli, Zuel, Italy, 1981), pages 77-101. Reidel. 

In Raff s PES for CH3 + HT, the potential is a sum of four three-center MLEPS potentials, one for each of the C-H-T moieties, and an angle-dependent term to control the change of the methyl moiety from trigonal planar to tetrahedral. By breaking up the potential in this manner. Raff reduced the problem of model1ing a six-body interaction to that of modelling several three-body ones. 

In mechanics, the inertial properties of a rotating rigid body are fully described by its inertial moment tensor I. We can simplify the subsequent equations if we employ in place of I the closely related planar moment tensor P, apparently first used by Kraitchman [4], At any stage of the calculations, however, an equivalent equation could be given which involves I instead of P. The principal planar moments P (g = x, y, z) are the three eigenvalues of the planar moment tensor P and the principal inertial moments Ig the eigenvalues of the inertial moment tensor I. Pg, Ig, and the rotational constants Bg = f/Ig are equivalent inertial parameters of the problem investigated (/conversion factor). 

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