<p>This 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).</p> / Thesis

For high speed vessels and offshore structures, wave impact, a main source of environmental loads, causes high local stresses and structural failure. However, the prediction of wave impact loads presents numerous challenges due to the complex nature of the instant structure-fluid interaction. The purpose of the present study is to develop an effective wave impact model to investigate the dynamic behaviors of specific shaped elements as they impact waves. To achieve this objective, a wave impact model with a body swinging on a pendulum system is developed. The body on the pendulum goes through a wave free surface driven by gravity at the pendulum's natural frequency. The system's motion and impact force during the entire oscillation time beginning from the instant of impact are of interest. The impact force is calculated by applying von Karman's method, which is based on momentum considerations. The usual wave forces are presented in the Morison's equation and incorporated into dynamic systems with other wave forces. For each body shape, the dynamic system is described by a strongly nonlinear ordinary differential equation and then solved by a Runge-Kutta differential equation solver. The dynamic response behavior and the impact force time history are obtained numerically and the numerical results show support the selection of a pendulum model as an efficient approach to study slamming loads. The numerical prediction of this model is compared to previous experiments and classification society codes. Moreover, a basic design of wave impact experiments using this pendulum model is proposed to provide a more accurate comparison between numerical results and experimental data for this model. This design will also serve as a first look at the experimental application of the pendulum model for the purpose of forecasting slamming force.

We use non-binary coding, elitist strategy, increasing mutation rate, extinction, and immigration strategy to improve the simple genetic algorithms in this study. We expect that the search technique can avoid falling into the local optimum due to the premature convergence, and purse the chance that finding the near-optimal parameters in the larger searching space could be obviously increased. We utilize SIRMs(Single Input Rule Modules) fuzzy controller for the stabilization control of inverted pendulum systems, and the dynamic importance degrees are built such that the angular control of the pendulum takes priority over the position control of the cart. We utilize modified genetic algorithms(MGA) to automatically tuning scaling factors of SIRMs fuzzy controller. From computer simulations, the pendulum control and the cart position control can fastly be stabilized.

Thesis (M.S.)--California State University, Chico. / Includes abstract. "Located in the Chico Digital Repository." Includes bibliographical references (p. 93-94).

The magnetic spherical pendulum is a mechanical system consisting of a pendulum whereof the bob is electrically charged, moving under the influence of gravitation and the magnetic field induced by a magnetic monopole deposited at the origin. Physically not directly realizable, it turns out to be equivalent to a reduction of the Lagrange top. This work is essentially the logbook of our attempts at understanding the simplest contemporary approaches to the magnetic spherical pendulum.

Thesis (M.S.)--Virginia Polytechnic Institute and State University, 1991. / Vita. Abstract. Includes bibliographical references (leaves 56-59). Also available via the Internet.

Thesis (Ph. D.)--University of Washington, 1998. / Vita. Includes bibliographical references (p. [89]-93).

Thesis (M.S.)--University of Missouri-Columbia, 2005. / The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file viewed on (January 23, 2007) Includes bibliographical references.

This thesis involves the analysis of four classes of nonlinear oscillators. We investigate a damped planar pendulum subject to vertical sinusoidal displacement of appropriate amplitude and frequency, a Hamiltonian planar pendulum with support point oscillating in the vertical direction, a forced spherical pendulum as a constrained dynamical system and a spinning double pendulum with the two masses oscillating in transversal planes. The motivation for this research was to understand and determine the fundamental dynamical properties of the four model systems. For this purpose analytical and numerical tools have been employed. Linearization, phase portraits, Poincare sections, basins of attraction, KAM theory, Lyapunov exponents and normal form theory have been considered as examples. For the damped planar pendulum a rigorous analysis is presented in order to show that, in the presence of friction, the upward equilibrium position becomes asymptotically stable. Furthermore, using numerical tools, the dynamics of the system far from its equilibrium points is systematically investigated. For the undamped and parametrically perturbed planar pendulum, we use KAM type arguments to rigorously prove the stability of the equilibrium point corresponding to the upside-down position. For the spherical pendulum a numerical framework is developed, which allows orbits to explore the entire sphere. We show that the qualitative change in the Poincare sections from regular to chaotic behaviour is in excellent qualitative agreement with corresponding computations of the Lyapunov exponents. Finally we study the dynamics of the spinning double pendulum by using normal form theory. We have identified the regions in physical parameter space where a codimension-two singularity occurs. An algorithm for the Cushman-Sanders normal form is constructed and analyzed. A representative model for the truncated normal form is presented.

The thesis deals with the planar problem regarding balancing of an inverted pendulum whose real model is situated in the laboratory A1/731a. The goal of this thesis is to build up the simulation model in the program Matlab Simulink and compare the attributes of the model with the real pendulum. The next step is to prove a regulation of the model in Matlab Simulink and find the way of controlling the real model by PLC on the basis of results found within the simulation.