In the last two decades, research on dynamics, vibration, and control has grown rapidly in most active scientific frontiers of science and technology, and it has been extended to diverse systems as well as applications in multidisciplinary areas. It is obvious that mathematical modeling, applied mathematics methods, and computational techniques play important roles in the recent development of this field. The Second International Conference on Dynamics, Vibration, and Control (ICDVC-2006) was held on 23–26 August 2006 in Beijing, China. The aim was to bring together scientists from the international community in the field of dynamics, vibration, and control to present their latest research work. The conference also provided an excellent forum for researchers from science and engineering, both experts and newcomers, to share ideas, experience, progress, and to explore new directions and problems in this fascinating area of science and technology in the 21st century. There were more than 300 participants from 18 countries and regions at this conference. The themes were intended to be broad enough so that mathematical theory, numerical simulation, physical experiments, engineering practices, information techniques, biological and financial activities, and other applications were included in the main programme.
The 12 articles in this special issue of International Journal of Computer Mathematics, entitled ‘Computer mathematics in dynamics and control’, were selected after rigorous peer-review from some of the high-quality presentations at the conference. These articles cover comprehensive aspects of computational and applied mathematics in dynamics and control of discrete and continuous systems in science and technology.
Two articles on the approximate solution for the KdV-Burgers equation and the modified Legendre rational spectral method for the Burgers equation are presented first. Then there are two articles related to non-smooth dynamics, including the algorithm of dark-curves and the identification and order of SSPOs of a piece-wise linear system modeling an actual gear system with impact and backlash and the linear complementary problem of dynamics of multi-rigid-body systems with friction.
There are two articles dedicated to the dynamics analysis and controller design of multi-body systems. An adjoint variable method of second sensitivity analysis is proposed for multi-body system dynamics described by second order differential/algebraic equations to improve the convergence of optimization design and simplify its computation. Then an optimal scheme for controller design is introduced for controlling the three-dimensional deployment process of a subsatellite involving a longitudinally flexible tether.
Two articles deal with dynamics of neural systems, that is, one for the non-resonant double Hopf bifurcation in a delayed neural network and the other for first-firing statistics of a neuron bombarded by additive coloured noise by using the stochastic averaging method. Then an article on a novel variable structure control strategy for a class of second-order nonlinear systems is presented based on the phase-plane analysis and used to stabilize non-holonomic systems in chained form.
Finally, three articles are concerned with the applications of chaos, including chaos control on the repeated Cournot game model in electric power duopoly, dynamic analysis of the game between land supply and housing prices as well as the effects of chaos, and an improved chaos optimization algorithm with its application in economic dynamics.
It is expected that all these articles will be beneficial to readers interested in further development in the field of dynamics and control.
As the guest editor, and on behalf of all the authors of this special issue, I sincerely thank Professor E.H. Twizell for his kind support and constant cooperation during the process of preparation and publication of this special issue. We acknowledge the reviewers who gave helpful comments and suggestions. We are grateful to the Natural Science Foundation of China (NSFC), the Chinese Society of Theoretical and Applied Mechanics (CSTAM), and all co-sponsors for their support of ICDVC-2006.