Orbitron. Part II. Magnetic levitation

TL;DR

This paper proves the existence of stable quasi-periodic motions of a magnetic dipole under combined magnetic and gravitational fields using Hamiltonian group-theoretic methods, supported by numerical simulations.

Contribution

It introduces a rigorous proof of stable motions in magnetic levitation systems using energy-momentum methods, expanding theoretical understanding.

Findings

Stable quasi-periodic motions are theoretically proven.

Numerical simulations confirm the feasibility of stable configurations.

Physically reasonable parameters can realize these stable motions.

Abstract

This paper devoted to proof the existence of stable quasi-periodic motions of the magnetic dipole that is under the action of the external magnetic field and homogeneous field of gravity. For proof this we used the group-theoretic methods of Hamiltonian mechanics, viz energy-momentum method. Numerical simulation shows the possibility of realization of stable motions with physically reasonable parameters of the system.