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Download IUTAM Symposium on Chaotic Dynamics and Control of Systems by Francis C. Moon (auth.), G. Rega, F. Vestroni (eds.) PDF

By Francis C. Moon (auth.), G. Rega, F. Vestroni (eds.)

The curiosity of the utilized mechanics group in chaotic dynamics of engineering platforms has exploded within the final fifteen years, even though examine task on nonlinear dynamical difficulties in mechanics begun good prior to the tip of the Eighties. It built first in the common context of the classical thought of nonlinear oscillations, or nonlinear vibrations, and of the proper engineering functions. This used to be a very fertile box by way of formula of mechanical and mathematical versions, of improvement of robust analytical thoughts, and of figuring out of a few uncomplicated nonlinear phenomena. At concerning the similar time, significant theoretical effects highlighting new resolution tools and new or advanced phenomena within the dynamics of deterministic structures have been got inside dynamical structures conception by way of subtle geometrical and computational strategies. in recent times, cautious experimental reviews were made to set up the particular incidence and observability of the expected dynamic phenomena, because it is vitally wanted in all engineering fields. advanced dynamics were proven to signify the behaviour of a good number of nonlinear mechanical platforms, starting from aerospace engineering functions to naval functions, mechanical engineering, structural engineering, robotics and biomechanics, and different parts. The overseas Union of Theoretical and utilized Mechanics grasped the significance of such complicated phenomena within the Eighties, while the 1st IUTAM Symposium dedicated to the final subject of nonlinear and chaotic dynamics in utilized mechanics and engineering was once held in Stuttgart (1989).

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Extra resources for IUTAM Symposium on Chaotic Dynamics and Control of Systems and Processes in Mechanics: Proceedings of the IUTAM Symposium held in Rome, Italy, 8–13 June 2003

Example text

To simplify this model further and to insure that the new ‘clock’ remains ticking near a period two cycle, we chose the A matrix to have the special form given above. When there is no coupling between the primitive machine and the new state variable x2 , (ε = 0) , the system exhibits a linear map in Chaotic clocks: A paradigm for the evolution of noise in machines 13 the additional state variable. Restricting the control parameter between zero and one guarantees an asymptotically stable fixed point with monotonic dynamics.

Voronov, “Adaptive backstepping with high-order tuner,” Automatica, 37, pp. 1953 – 1960, 2001. [19] F. Moon, Chaotic and Fractal Dynamics. An Introduction for Applied Scientists and Engineers. Wiley, 1992. [20] G. Nikolis and I. R. Prigogine, Self-Organization in Non-Equilibrium Systems. Wiley, New York, 1977. V. S. Oziraner, Stability and stabilization of motion with respect to part of variables. Moscow, Nauka. P. 263, 1987, (in Russian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± © 2005 Springer.

19] F. Moon, Chaotic and Fractal Dynamics. An Introduction for Applied Scientists and Engineers. Wiley, 1992. [20] G. Nikolis and I. R. Prigogine, Self-Organization in Non-Equilibrium Systems. Wiley, New York, 1977. V. S. Oziraner, Stability and stabilization of motion with respect to part of variables. Moscow, Nauka. P. 263, 1987, (in Russian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± © 2005 Springer.

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