On homoclinic chaos and a control chaos strategy applied to a free-joint nonholonomic manipulator

In this work, the occurrence of chaos (homoclinic scene) is verified in a robotic system with two degrees of freedom by using Poincare-Mel'nikov method. The studied problem was based on experimental results of a two-joint planar manipulator-first joint actuated and the second joint free-that resides in a horizontal plane. This is the simplest model of nonholonomic free-joint manipulators. The purpose of the present study is to verify analytically those results and to suggest a control strategy.

On stick-slip homoclinic chaos and bifurcations in a mechanical system with dry friction

In this paper we consider a self-excited mechanical system by dry friction in order to study the bifurcational behavior of the arisen vibrations. The oscillating system consists of a mass block-belt-system which is self-excited by static and Coulomb friction. We analyze the system behavior numerically through bifurcation diagrams, phase portraits, frequency spectra and Poincare maps, which show the existence of nonhomoclinic and homoclinic chaos and a route to homoclinic chaos. The homoclinic chaos is also analyzed analytically via the Melnikov prediction method. The system dynamic is characterized by the existence of two potential wells in the phase plane which exhibit rich bifurcational and chaotic behavior.

A comment on a nonideal centrifugal vibrator machine behavior with soft and hard springs

This paper concerns a type of rotating machine (centrifugal vibrator), which is supported on a nonlinear spring. This is a nonideal kind of mechanical system. The goal of the present work is to show the striking differences between the cases where we take into account soft and hard spring types. For soft spring, we prove the existence of homoclinic chaos. By using the Melnikov's Method, we show the existence of an interval with the following property: if a certain parameter belongs to this interval, then we have chaotic behavior; otherwise, this does not happen. Furthermore, if we use an appropriate damping coefficient, the chaotic behavior can be avoided. For hard spring, we prove the existence of Hopf's Bifurcation, by using reduction to Center Manifolds and the Bezout Theorem (a classical result about algebraic plane curves).

On chaotic behavior of a fixed offshore structure

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Time-periodic perturbation of a Lienard equation with an unbounded homoclinic loop

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Relaxation-chaos phenomena in celestial mechanics. I. On wisdom's model for the 3/1 kirkwood gap

Sudden eccentricity increases of asteroidal motion in 3/1 resonance with Jupiter were discovered and explained by J. Wisdom through the occurrence of jumps in the action corresponding to the critical angle (resonant combination of the mean motions). We pursue some aspects of this mechanism, which could be termed relaxation-chaos: that is, an unconventional form of homoclinic behavior arising in perturbed integrable Hamiltonian systems for which the KAM theorem hypothesis do not hold. © 1987.

Finding order in chaos : a problem based collaborative assignment for 1300 students across 19 disciplines

The use of collaborative assignments for assessment is a risky undertaking for students and course designers. Yet the benefits, in terms of core learning outcomes, competencies, collaborative sense making and student involvement, suggest that the effort is worthwhile. Formal descriptions and rules do little to ameliorate the perception of risk and increased anxiety by students. (Ryan, 2007). BEB100 Introducing Professional Learning is a faculty-wide foundation unit with over 1300 students from 19 disciplines across the Faculty of the Built Environment and Engineering (“BEE”) at the Queensland University of Technology (“QUT”), Brisbane, Australia. Finding order in chaos outlines the approach and justification, assessment criteria, learning resources, teamwork tools, tutorial management, communication strategies, 2007-09 Student Learning Experience Survey results, annual improvements, findings and outcomes.

Guided chaos : path planning and control for a UAV-forced landing

In recent years, unmanned aerial vehicles (UAVs) have been widely used in combat, and their potential applications in civil and commercial roles are also receiving considerable attention by industry and the research community. There are numerous published reports of UAVs used in Earth science missions [1], fire-fighting [2], and border security [3] trials, with other speculative deployments, including applications in agriculture, communications, and traffic monitoring. However, none of these UAVs can demonstrate an equivalent level of safety to manned aircraft, particularly in the case of an engine failure, which would require an emergency or forced landing. This may be arguably the main factor that has prevented these UAV trials from becoming full-scale commercial operations, as well as restricted operations of civilian UAVs to only within segregated airspace.

Controlling chaos? The value and the challenges of applying complexity theory to project management

The literature abounds with descriptions of failures in high-profile projects and a range of initiatives has been generated to enhance project management practice (e.g., Morris, 2006). Estimating from our own research, there are scores of other project failures that are unrecorded. Many of these failures can be explained using existing project management theory; poor risk management, inaccurate estimating, cultures of optimism dominating decision making, stakeholder mismanagement, inadequate timeframes, and so on. Nevertheless, in spite of extensive discussion and analysis of failures and attention to the presumed causes of failure, projects continue to fail in unexpected ways. In the 1990s, three U.S. state departments of motor vehicles (DMV) cancelled major projects due to time and cost overruns and inability to meet project goals (IT-Cortex, 2010). The California DMV failed to revitalize their drivers’ license and registration application process after spending $45 million. The Oregon DMV cancelled their five year, $50 million project to automate their manual, paper-based operation after three years when the estimates grew to $123 million; its duration stretched to eight years or more and the prototype was a complete failure. In 1997, the Washington state DMV cancelled their license application mitigation project because it would have been too big and obsolete by the time it was estimated to be finished. There are countless similar examples of projects that have been abandoned or that have not delivered the requirements.

Bispectral and trispectral characterization of transition to chaos in the Duffing oscillator

Higher-order spectral (bispectral and trispectral) analyses of numerical solutions of the Duffing equation with a cubic stiffness are used to isolate the coupling between the triads and quartets, respectively, of nonlinearly interacting Fourier components of the system. The Duffing oscillator follows a period-doubling intermittency catastrophic route to chaos. For period-doubled limit cycles, higher-order spectra indicate that both quadratic and cubic nonlinear interactions are important to the dynamics. However, when the Duffing oscillator becomes chaotic, global behavior of the cubic nonlinearity becomes dominant and quadratic nonlinear interactions are weak, while cubic interactions remain strong. As the nonlinearity of the system is increased, the number of excited Fourier components increases, eventually leading to broad-band power spectra for chaos. The corresponding higher-order spectra indicate that although some individual nonlinear interactions weaken as nonlinearity increases, the number of nonlinearly interacting Fourier modes increases. Trispectra indicate that the cubic interactions gradually evolve from encompassing a few quartets of Fourier components for period-1 motion to encompassing many quartets for chaos. For chaos, all the components within the energetic part of the power spectrum are cubically (but not quadratically) coupled to each other.

Cultural chaos : Journalism, News and Power in a Globalised World

With examples drawn from media coverage of the War on Terror, the 2003 invasion of Iraq, Hurricane Katrina and the London underground bombings, Cultural Chaos explores the changing relationship between journalism and power in an increasingly globalised news culture. In this new text, Brian McNair examines the processes of cultural, geographic and political dissolution in the post-Cold War era and the rapid evolution of information and communication technologies. He investigates the impact of these trends on domestic and international journalism and on political processes in democratic and authoritarian societies across the world. Written in a lively and accessible style, Cultural Chaos provides students with an overview of the evolution of the sociology of journalism, a critical review of current thinking within media studies and an argument for a revision and renewal of the paradigms that have dominated the field since the early twentieth century. Separate chapters are devoted to new developments such as the rise of the blogosphere and satellite television news and their impact on journalism more generally. Cultural Chaos will be essential reading for all those interested in the emerging globalised news culture of the twenty-first century.