1997/07/23 by Sang-Yoon Kim, Kim, Sang-Yoon, S. H. Shin +8
Computer Science · Engineering · Physics and Astronomy · #Chaos control and synchronization #Chaotic Dynamics (nlin.CD) #Computational Physics and Python Applications #Condensed Matter (cond-mat) #FOS: Physical sciences #Magnetic Bearings and Levitation Dynamics #chao-dyn #cond-mat #nlin.CD
paper · pdf · doi:10.48550/arxiv.chao-dyn/9707017
RevTeX, 7 eps figures included in this revised version
arxiv created 1997/07/23 · openalex publication_date 1997/07/23 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
An experimental study of bifurcations associated with stability of stationary points (SP's) in a parametrically forced magnetic pendulum and a comparison of its results with numerical results are presented. The critical values for which the SP's lose or gain their stability are experimentally measured by varying the two parameters Ω (the normalized natural frequency) and A (the normalized driving amplitude). It is observed that, when the amplitude A exceeds a critical value, the normal SP with θ=0 (θ is the angle between the permanent magnet and the magnetic field) becomes unstable either by a period-doubling bifurcation or by a symmetry-breaking pitchfork bifurcation, depending on the values of Ω. However, in contrast with the normal SP the inverted SP with θ=π is observed to become stable as A is increased above a critical value by a pitchfork bifurcation, but it also destabilizes for a higher critical value of A by a period-doubling bifurcation. All of these experimental results agree well with numerical results obtained using the Floquet theory.