Abrarov Dmitry. General Solution Exp ζ(s,∆_12 (q)) Of The Euler-poisson Equations As The Solution Of The Functional Quaternionic Q-pendulum And Canonical Functional Exponent


Natural Sciences / Mathematics / Dynamical systems

Submitted on: Feb 28, 2022, 07:39:31

Description: The work structures, details and develops the argumentation and the applied value of the effect of exact solvability of the Euler-Poisson equations, revealed in monograph [1]. The most essential assertations are proved in [1], the proofs of the other assertations are either discussed or outlined. An essential new circumstance is that an equivariant analytic Galois solvable structure (connection) on the group SO(3) induces a canonical analytic functional connection on the space of classical quaternions. Such a connection on the emerging space of functional quaternions has a canonical L-functional potential over the field ℂ in the form of a function exp I(s,∆_12 (q)), which is a general solution of the original equations and represents canonical functional exponent. The revealed functional quaternionic nature of the Euler-Poisson equations canonically leads to their integrability on the coadjoint representation of the algebra e_8 (Q(s)). This algebra is a canonical simply connected functional extension of the simple exceptional algebra e_8, defined over the field of rational functions over C(s) and is isomorphic to central symmetry in 5-dimensional Euclidean space. It is paradoxical that these equivariant functional symmetries represent the phase flow of the canonical analytic pendulum with the canonical angular coordinate represented by the automorphic modular cusp form ∆_12 (q) of weight 12. The phase flow of this pendulum is isomorphic to 281-dimensional special orthogonal group SO(281,R) and is an orthogonal representation of the functional exponent. This symmetry has the mechanical meaning of the inertial rotation of the rotor in a fully stabilized gimbal. The number 281 (Ryazantsev's constant from QFT) is the number of degrees of freedom of this universal gyroscope. This mechanical system is the mechanical interpretation of the general solution of the Euler-Poisson equations. The coordination of this symmetry gives an explicit analytical form of the...

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