Application of the Quaternionic Self-Oscillation Apparatus for the Description of Planetary Dynamics

Abstract

Arunas Ostasevicius

An alternative conceptual framework for describing the dynamics of celestial bodies is presented, based on the theory of non-linear self-oscillations within an active material cosmic medium. From first principles—Boltzmann’s kinetic equation and Verhulst non-linear logistic dynamics—a distributed quaternionic equation of motion is rigorously derived. The orbital motion of the planetary center of mass and its axial rotation are proven to be stable phase attractors (limit cycles) within absolute Euclidean Hamilton space. Using the analytical method of phase averaging, the secular deformation of Mercury’s trajectory under the influence of polytropic medium compression near the Sun is calculated. The methodological superiority of the non-linear dynamics of open media over the metric geometrization of spacetime in General Relativity is demonstrated, allowing for the complete elimination of cumbersome tensor algebra and the postulation of arbitrary initial conditions.

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