Periodic nonlinear sliding modes for two uniformly magnetized spheres.
Chaos
; 27(5): 053107, 2017 May.
Article
en En
| MEDLINE
| ID: mdl-28576112
A uniformly magnetized sphere slides without friction along the surface of a second, identical sphere that is held fixed in space, subject to the magnetic force and torque of the fixed sphere and the normal force. The free sphere has two stable equilibrium positions and two unstable equilibrium positions. Two small-amplitude oscillatory modes describe the sliding motion of the free sphere near each stable equilibrium, and an unstable oscillatory mode describes the motion near each unstable equilibrium. The three oscillatory modes remain periodic at finite amplitudes, one bifurcating into mixed modes and circumnavigating the free sphere at large energies. For small energies, the free sphere is confined to one of the two discontiguous domains, each surrounding a stable equilibrium position. At large energies, these domains merge and the free sphere may visit both positions. The critical energy at which these domains merge coincides with the cumulation point of an infinite cascade of mixed-mode bifurcations. These findings exploit the equivalence of the force and torque between two uniformly magnetized spheres and the force and torque between two equivalent point dipoles, and offer clues to the rich nonlinear dynamics of this system. Online MagPhyx visualizations illustrate the dynamics.
Texto completo:
1
Colección:
01-internacional
Base de datos:
MEDLINE
Idioma:
En
Revista:
Chaos
Asunto de la revista:
CIENCIA
Año:
2017
Tipo del documento:
Article
País de afiliación:
Estados Unidos
Pais de publicación:
Estados Unidos