A simple magnetic oscillator-rotator model made of magnetic balls, and its examination by video-analysis

Abstract

We built a simple structure of seven dipole neodymium magnetic balls, a magnetic spinner that easily rotates around its central ball. This proved to be a very simple magnetic oscillator-rotator with a dipole-like field. After capturing videos of its rotating movements in different magnetic fields, video analysis has provided us with the rotation angle-time function of the motion, either in the case of a stationary magnetic field (damped oscillation) or an alternating magnetic field (forced oscillations). We were able to obtain a numerical solution for the differential equation describing the motion, a solution which was in tune with the special phenomena observed. It was especially interesting—and can be utilised in physics education—that the oscillation of the system was very strongly dependent on the initial conditions and seemed to be quite chaotic. The rotation angle, angular speed functions and their representation in phase space have shown the characteristics of chaotic behaviour, especially in the case of coupled oscillations. Thus, this kind of chaotic movement can be demonstrated very simply, even in classroom conditions by the use of such magnetic systems. At the same time, such models might help in the scientific understanding of magnetic nanostructures—their self-assembly and motions in alternating magnetic fields—which is the basis of practical applications such as magnetic hyperthermia.

Subtle dynamics of the chaotic torsion pendulum: a detailed comparison between experiments and numerical simulations

“…The seeming contradiction between the deterministic process and the unpredictable behavior of chaos offers an interesting and valuable general insight into the nonlinear nature of the world. Research on the topic of chaos is flourishing since its discovery, not only from the perspective of advanced science [2][3][4][5][6][7], but also from an educational point of view [8][9][10][11][12][13][14][15][16][17][18][19][20][21]. Many excellent introductory monographs that explain basic concepts of chaos exist [8][9][10][11][12][13][14][15], as well as various elaborate devices [16][17][18][19][20][21] that vividly depict the dynamical feature of a chaotic system.…”

“…Research on the topic of chaos is flourishing since its discovery, not only from the perspective of advanced science [2][3][4][5][6][7], but also from an educational point of view [8][9][10][11][12][13][14][15][16][17][18][19][20][21]. Many excellent introductory monographs that explain basic concepts of chaos exist [8][9][10][11][12][13][14][15], as well as various elaborate devices [16][17][18][19][20][21] that vividly depict the dynamical feature of a chaotic system. In college-level physics courses, one of the standard devices for exhibiting chaotic behavior is the chaotic torsion pendulum (CTP) [22][23][24][25].…”

Wilberforce pendulum: modelling linearly damped coupled oscillations of a spring-mass system

“…Due to their interesting behaviour and widespread applications in various fields, coupled oscillators have long been a research interest. Many involve masses attached to springs [1][2][3][4][5] or masses oscillating in a magnetic field [6][7][8][9][10]. There are also more unique ones that exhibit parametric resonance [11,12].…”