Experimental bifurcation control of a parametric pendulum

Acknowledgments The authors would like to thank the Brazilian Research Agencies CNPq, CAPES and FAPERJ and through the INCT-EIE (National Institute of Science and Technology - Smart Structures in Engineering) the CNPq and FAPEMIG for their support. The Air Force Office of Scientific Research (AFOSR) is also acknowledged. Funding The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The authors would like to acknowledge the support of ANP, FINEP and MCT through PRH-PB/MCT, and also the support of Petrobras. The authors also would like to thank the Brazilian Research Agencies CNPq, CAPES and FAPERJ and through the INCT-EIE (National Institute of Science and Technology - Smart Structures in Engineering) the CNPq and FAPEMIG for their support. The Air Force Office of Scientific Research (AFOSR) is also acknowledged.Peer reviewedPostprin

The dynamics of the pendulum suspended on the forced Duffing oscillator

We investigate the dynamics of the pendulum suspended on the forced Duffing oscillator. The detailed bifurcation analysis in two parameter space (amplitude and frequency of excitation) which presents both oscillating and rotating periodic solutions of the pendulum has been performed. We identify the areas with low number of coexisting attractors in the parameter space as the coexistence of different attractors has a significant impact on the practical usage of the proposed system as a tuned mass absorber.Comment: Accepte

Tilted excitation implies odd periodic resonances

This work was supported by the Brazilian agencies FAPESP and CNPq. MSB also acknowledges the Engineering and Physical Sciences Research Council grant Ref. EP/I032606/1. GID thanks Felipe A. C. Pereira for fruitful discussions.Peer reviewedPostprin

Synchronous motion of two vertically excited planar elastic pendula

The dynamics of two planar elastic pendula mounted on the horizontally excited platform have been studied. We give evidence that the pendula can exhibit synchronous oscillatory and rotation motion and show that stable in-phase and anti-phase synchronous states always co-exist. The complete bifurcational scenario leading from synchronous to asynchronous motion is shown. We argue that our results are robust as they exist in the wide range of the system parameters.Comment: Submitte

Characterization in bi-parameter space of a non-ideal oscillator

The authors thank scientific agencies CAPES, CNPq (112952/2015-1), and FAPESP (2011/ 19269-11). M. S. Baptista also thanks EPSRC (EP/I03 2606/1).Peer reviewedPostprin

Non-stationary resonance dynamics of the harmonically forced pendulum

The stationary and highly non-stationary resonant dynamics of the harmonically forced pendulum are described in the framework of a semi-inverse procedure combined with the Limiting Phase Trajectory concept. This procedure, implying only existence of slow time scale, permits one to avoid any restriction on the oscillation amplitudes. The main results relating to the dynamical bifurcation thresholds are represented in a closed form. The small parameter defining the separation of the time scales is naturally identified in the ana- lytical procedure. Considering the pendulum frequency as the control parameter we reveal two qualitative tran- sitions. One of them corresponding to stationary instability with formation of two additional stationary states, the other, associated with the most intense energy drawing from the source, at which the amplitude of pendulum oscillations abruptly grows. Analytical predictions of both bifurcations are verified by numerical integration of original equation. It is also shown that occurrence of chaotic domains may be strongly connected with the second transition

Supercritical bifurcation of a hula hoop

The motion of a hoop hung on a spinning wire provides an illustrative and pedagogical example of a supercritical bifurcation. Above a certain angular velocity threshold Omega_c, the hoop rises, making an angle theta = (Omega-Omega_c)^(1/2) with the vertical. The equation of motion is derived in the limit of a long massless wire, and the calculated steady states are compared to experimental measurements. This simple experiment is suitable for classroom demonstration, and provides an interesting alternative to the classical experiment of the bead sliding on a rotation hoop.Comment: subm. to Am. J. Phys. (7 figs