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The theme of this book is the philosophy that any particle flow generates a particle dynamics, in a suitable geometrical framework. It introduces the reader in a gradual and accessible manner to this subject, covering topics that include: geometrical and physical vector fields; field lines; flows; stability of equilibrium points; potential systems and catastrophe geometry; field hypersurfaces; bifurcations; distribution orthogonal to a vector field; extrema with nonholonomic constraints; thermodynamic systems; energies; geometric dynamics induced by a vector field; magnetic fields around piecewise rectilinear electric circuits; geometric magnetic dynamics; and granular materials and their mechanical behavior. Primary audience: First-year graduate students in mathematics, mechanics, physics, engineering, biology, chemistry, economics. Part of the book can be used for undergraduate students. Secondary audience: The book is addressed also to professors and researchers whose work involves mathematics, mechanics, physics, engineering, biology, chemistry, and economics.
|Vector Fields||p. 1|
|Particular Vector Fields||p. 35|
|Field Lines||p. 63|
|Stability of Equilibrium Points||p. 117|
|Potential Differential Systems of Order One and Catastrophe Theory||p. 145|
|Field Hypersurfaces||p. 177|
|Bifurcation Theory||p. 201|
|Submanifolds Orthogonal to Field Lines||p. 225|
|Dynamics Induced by a Vector Field||p. 273|
|Magnetic Dynamical Systems and Sabba Stefanescu Conjectures||p. 303|
|Bifurcations in the Mechanics of Hypoelastic Granular Materials||p. 357|
|Table of Contents provided by Blackwell. All Rights Reserved.|
Series: Mathematics and Its Applications
Weight (kg): 0.866