Geometric dynamics
著者
書誌事項
Geometric dynamics
（Mathematics and its applications, v. 513）
Kluwer Academic, c2000
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注記
Includes bibliographical references and index
内容説明・目次
内容説明
The theme of this text is the philosophy that any particle flow generates a particle dynamics, in a suitable geometrical framework. It covers 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 behaviour. The text should be useful for first-year graduate students in mathematics, mechanics, physics, engineering, biology, chemistry, and economics. It can also be addressed to professors and researchers whose work involves mathematics, mechanics, physics, engineering, biology, chemistry, and economics.
目次
- Preface. 1. Vector Fields. 2. Particular Vector Fields. 3. Field Lines. 4. Stability of Equilibrium Points. 5. Potential Differential Systems of Order One and Catastrophe Theory. 6. Field Hypersurfaces. 7. Bifurcation Theory. 8. Submanifolds Orthogonal to Field Lines. 9. Dynamics Induced by a Vector Field. 10. Magnetic Dynamical Systems and Sabba Stefanescu Conjectures. 11. Bifurcations in the Mechanics of Hypoelastic Granular Materials
- L. Dragusin. Bibliography. Index.
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