Quaternions in Hamiltonian dynamics of a rigid body -- Part III. Asymmetric Top in the Orbitron

TL;DR

This paper models the Hamiltonian dynamics of an asymmetric top using quaternions within a magnetic field, analyzing stability near symmetric configurations through simulations.

Contribution

It introduces a quaternion-based Poisson structure for asymmetric tops in magnetic fields and studies stability near symmetric states using Monte Carlo simulations.

Findings

Stability persists near symmetric configurations.

Quaternion Poisson structure effectively models the dynamics.

Monte Carlo simulations validate theoretical stability results.

Abstract

The Poisson structure in the quaternion variables was proposed for asymmetric top in the external axially symmetric magnetic field. For that model of interaction the motion equation were got. The model was simulated in the neighbourhood of a relative equilibrium of the symmetric top -- Orbitron by Monte Carlo method. For small deviations with respect to the symmetry we observe the persistence of the stability.