# Abrarov Dmitry. Relativistic pendulum-oscillator model of the Earth-moon system

## Natural Sciences / Mathematics / Dynamical systems

Submitted on: Mar 30, 2023, 12:38:01

Description: A paradoxical formally one degree of freedom model of the relative dynamics of the Earth-Moon system is proposed, which ideologically goes back to P.L. Kapitsa. This model represents the canonical relativistic ball - a general simply connected analytical perturbation of a homogeneous geometric ball over complex time â„‚. This Hamiltonian system exactly represents a single-degree analytical Hamiltonian system - the phase flow of a mathematical pendulum in strictly vertical equilibrium over â„‚ , or equivalently, the phase flow of a canonical analytical oscillator.. This model is a canonical pendulum-oscillatory normalization of the analytic continuation to infinity of the formal time of the general classical Euler-Poisson equations phase flow over â„‚. Therefore, we call this model the âEśpendulum-oscillatorâEť model. The Euler-Poisson (EP) equations within the framework of this one degree of freedom model are realized by the well-known PainlevĂ© VI equation. The Earth and the Moon are modeled by a gravitational balls dipole with its centers at the ends of the analytical oscillator and are residues of the L-functional Hamiltonian of the oscillator with a physically meaningful relativistic structure. The gravitational dipole is the canonical invariant set of a simply connected 2-sheeted covering of the three-dimensional sphere S^3 (C) by a mapping of the autorecursive time reversibility symmetry of the general EP equations over C-time. Within the framework of the pendulum-oscillator model, by analyzing the structure of residues in its singularities, the following are realized: a mathematically and mechanically necessary correction of the classical explanation of the Dzhanibekov effect (as the canonical global parametrization of sphere S^3 (C)), an explanation of the orientational stability of the rotations of the Earth and the Moon, a qualitative explanation of the Chandler effect of the movement of the poles (the axes of own rotation) of the Earth and Moon. Ba...

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