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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.

Preface
Vector Fieldsp. 1
Particular Vector Fieldsp. 35
Field Linesp. 63
Stability of Equilibrium Pointsp. 117
Potential Differential Systems of Order One and Catastrophe Theoryp. 145
Field Hypersurfacesp. 177
Bifurcation Theoryp. 201
Submanifolds Orthogonal to Field Linesp. 225
Dynamics Induced by a Vector Fieldp. 273
Magnetic Dynamical Systems and Sabba Stefanescu Conjecturesp. 303
Bifurcations in the Mechanics of Hypoelastic Granular Materialsp. 357
Bibliographyp. 385
Indexp. 393
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780792364016
ISBN-10: 0792364015
Series: Mathematics and Its Applications
Audience: Professional
Format: Hardcover
Language: English
Weight (kg): 0.866