Browsing by Subject "Pendulum"
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Item Open Access Dynamics of the Disk-Pendulum Coupled System With Vertical Excitation(2016) Wang, XuesheThis paper investigates the static and dynamic characteristics of the semi-elliptical rocking disk on which a pendulum pinned. This coupled system’s response is also analyzed analytically and numerically when a vertical harmonic excitation is applied to the bottom of the rocking disk. Lagrange’s Equation is used to derive the motion equations of the disk-pendulum coupled system. The second derivative test for the system’s potential energy shows how the location of the pendulum’s pivotal point affects the number and stability of equilibria, and the change of location presents different bifurcation diagrams for different geometries of the rocking disk. For both vertically excited and unforced cases, the coupled system shows chaos easily, but the proper chosen parameters can still help the system reach and keep the steady state. For the steady state of the vertically excited rocking disk without a pendulum, the variation of the excitation’s amplitude and frequency result in the hysteresis for the amplitude of the response. When a pendulum is pinned on the rocking disk, three major categories of steady states are presently in the numerical way.
Item Open Access Nonsmooth Dynamics in Two Interacting, Impacting Pendula(2012) George, Christopher MichaelThis thesis reviews the experimental investigation of a non-smooth dynamical system consisting of two pendula; a large pendulum attached to a frame with an impact wall, and a small pendulum, which shares its axis of rotation with the large pendulum and can impact against the large pendulum. The system is forced with a sinusoidal horizontal motion, and due to the nonlinearities present in pendula as well as the discontinuous forcing from impacts, exhibits a wide range of behavior. Periodic, quasi-periodic, and chaotic responses all are possible, hysteresis is present, and grazing bifurcations allow for spontaneous change of behavior and the appearance of chaotic responses without following a traditional route to chaos. This thesis follows from existing non-linear dynamics research on forced pendula, impacting systems (such as a bouncing ball) and doubly impacting systems (ball bouncing on top of a bouncing ball).
Item Open Access The Pit and the Pendulum, Dramatic Cantata for Baritone, Chamber Ensemble, Male Choir and Electronics; Formal Plan and Constructive Principles of the Heterophonic Textures in Berio’s Coro.(2021) Amici, MaximilianoThis dissertation consists of two parts: the artistic part is a dramatic cantata for Baritone, Chamber Ensemble, Male Choir and Electronics. The scholarly part is an article which inquires into compositional aspects of Luciano Berio’s choral and symphonic piece Coro.Chapter 1 presents The Pit and the Pendulum, a dramatic cantata, in full score. Using the enhanced sonic environment allowed by the superimposition of vocal and acoustic music with a fantastic landscape created by means of electronic sounds, my composition explores the themes of Poe’s story. The tale, full of powerful metaphoric images, could be seen as a description of the experience of imprisonment. The pendulum descending from the ceiling, beyond being a clear metaphor of the inexorable passing of time, was actually one of the tortures used by the Spanish Inquisition. The blazing walls directly recall instruments of torture used at the time, as well. Nonetheless, the pit, whose black abyss is a symbol of indeterminacy, seems to point us to the annihilation of our conscience, typical of the most brutal torture of every kind and era. Victims of torture normally succumb to delirium though isolation, starvation and the alternation of torture and respite. On the brink of the pit, faced with the blackness of death, the mind of the condemned is, in this case, pushed beyond its limits and, ironically, he becomes able to conceive things that otherwise would be beyond his intellective and emotional faculties. From this terrible experience, in Poe’s tale, the prisoner gains the intuition and the knowledge of a deeper inner reality. In this regard, The Pit and the Pendulum is a tale of salvation and growth, against all odds. Chapter 2 presents the theoretical part of the dissertation, “Formal Plan and Constructive Principles of the Heterophonic Textures in Berio’s Coro.” This analytic essay on the large choral/symphonic work Coro, written in 1976 by Luciano Berio, is based on my study of his manuscripts preserved at the Paul Sacher Foundation in Basel. I was able to consult the archive in June 2019. The article explores Berio’s motives in his placement of the choir in relation to the orchestra onstage, its premises and its consequences from a compositional point of view. It also investigates the relation between Berio’s music and the work of the ethnomusicologist Simha Arom on central African music, which inspired the composition. Thanks to some sketches left by the composer, I have been able to reconstruct the motivation behind some of the most significant compositional choices of the piece as well as several compositional procedures used by the composer to present and develop his musical discourse. In Chapter 3 the aesthetic and scholarly conclusions of this dissertation are summarized.