Geometric Dynamics by C. UdristeGeometric Dynamics by C. Udriste

Geometric Dynamics

byC. Udriste

Paperback | October 23, 2012

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Geometric dynamics is a tool for developing a mathematical representation of real world phenomena, based on the notion of a field line described in two ways: -as the solution of any Cauchy problem associated to a first-order autonomous differential system; -as the solution of a certain Cauchy problem associated to a second-order conservative prolongation of the initial system. The basic novelty of our book is the discovery that a field line is a geodesic of a suitable geometrical structure on a given space (Lorentz-Udri<_te20_world-force20_law29_.20_in20_other20_words2c_20_we20_create20_a20_wider20_class20_of20_riemann-jacobi2c_20_riemann-jacobi-lagrange2c_20_or20_finsler-jacobi20_manifolds2c_20_ensuring20_that20_all20_trajectories20_of20_a20_given20_vector20_field20_are20_geodesics.20_this20_is20_our20_contribution20_to20_an20_old20_open20_problem20_studied20_by20_h.20_poincare2c_20_s.20_sasaki20_and20_others.20_from20_the20_kinematic20_viewpoint20_of20_corpuscular20_intuition2c_20_a20_field20_line20_shows20_the20_trajectory20_followed20_by20_a20_particle20_at20_a20_point20_of20_the20_definition20_domain20_of20_a20_vector20_field2c_20_if20_the20_particle20_is20_sensitive20_to20_the20_related20_type20_of20_field.20_therefore2c_20_field20_lines20_appear20_in20_a20_natural20_way20_in20_problems20_of20_theoretical20_mechanics2c_20_fluid20_mechanics2c_20_physics2c_20_thermodynamics2c_20_biology2c_20_chemistry2c_20_etc. world-force="" _law29_.="" in="" other="" _words2c_="" we="" create="" a="" wider="" class="" of="" _riemann-jacobi2c_="" _riemann-jacobi-lagrange2c_="" or="" finsler-jacobi="" _manifolds2c_="" ensuring="" that="" all="" trajectories="" given="" vector="" field="" are="" geodesics.="" this="" is="" our="" contribution="" to="" an="" old="" open="" problem="" studied="" by="" h.="" _poincare2c_="" s.="" sasaki="" and="" others.="" from="" the="" kinematic="" viewpoint="" corpuscular="" _intuition2c_="" line="" shows="" trajectory="" followed="" particle="" at="" point="" definition="" domain="" _field2c_="" if="" sensitive="" related="" type="" field.="" _therefore2c_="" lines="" appear="" natural="" way="" problems="" theoretical="" _mechanics2c_="" fluid="" _physics2c_="" _thermodynamics2c_="" _biology2c_="" _chemistry2c_="">
Title:Geometric DynamicsFormat:PaperbackDimensions:395 pagesPublished:October 23, 2012Publisher:Springer-Verlag/Sci-Tech/TradeLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:9401058229

ISBN - 13:9789401058223

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Table of Contents

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.