In 2008, November 23-28, the workshop of ”Classical Problems on Planar Polynomial Vector Fields ” was held in the Banff International Research Station, Canada. Called "classical problems", it was concerned with the following: (1) Problems on integrability of planar polynomial vector fields. (2) The problem of the center stated by Poincaré for real polynomial differential systems, which asks us to recognize when a planar vector field defined by polynomials of degree at most n possesses a singularity which is a center. (3) Global geometry of specific classes of planar polynomial vector fields. (4) Hilbert’s 16th problem. These problems had been posed more than 110 years ago. Therefore, they are called "classical problems" in the studies of the theory of dynamical systems. The qualitative theory and stability theory of differential equations, created by Poincaré and Lyapunov at the end of the 19th century, had major developments as two branches of the theory of dynamical systems during the 20th century. As a part of the basic theory of nonlinear science, it is one of the very active areas in the new millennium. This book presents in an elementary way the recent significant developments in the qualitative theory of planar dynamical systems. The subjects are covered as follows: the studies of center and isochronous center problems, multiple Hopf bifurcations and local and global bifurcations of the equivariant planar vector fields which concern with Hilbert’s 16th problem. The book is intended for graduate students, post-doctors and researchers in dynamical systems. For all engineers who are interested in the theory of dynamical systems, it is also a reasonable reference. It requires a minimum background of a one-year course on nonlinear differential equations.
X-by-wire Unmanned Ground Vehicles (UGVs) have been attracting increased attention for various civilian or military applications. The x-by-wire techniques (drive-by-wire, steer-by-wire, and brake-by-wire techniques) provide the possibility of achieving novel vehicle design and advanced dynamics control, which can significantly improve the overall performance, maneuverability, and mobility of the UGVs. However, there are few full x-by-wire UGVs prototype models reported in the world. Therefore, there is no book that can fully describe the design, configuration, and dynamics control approach of full x-by-wire UGVs, which makes it difficult for readers to study this hot and interesting topic. In this book, we use a full x-by-wire UGV, developed by our group, as the example. This UGV is completely x-by-wire with four in-wheel motors driven and a four-wheel independent steer steer. In this book, the overall design of the UGV, the design of the key subsystems (battery pack system, in-wheel motor-driven system, independent steer system, remote and autonomous control system), and the dynamics control approach will be introduced in detail, and the experiment's results will be provided to validate the proposed dynamics control approach.
This book presents in an elementary way the recent significant developments in the qualitative theory of planar dynamical systems. The subjects are covered as follows: the studies of center and isochronous center problems, multiple Hopf bifurcations and local and global bifurcations of the equivariant planar vector fields which concern with Hilbert's 16th problem. This book is intended for graduate students, post-doctors and researchers in the area of theories and applications of dynamical systems. For all engineers who are interested the theory of dynamical systems, it is also a reasonable reference. It requires a minimum background of an one-year course on nonlinear differential equations.
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