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© 2000

Geometric Dynamics

Book

Part of the Mathematics and Its Applications book series (MAIA, volume 513)

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Constantin Udrişte
    Pages 1-33
  3. Constantin Udrişte
    Pages 35-61
  4. Constantin Udrişte
    Pages 63-116
  5. Constantin Udrişte
    Pages 117-144
  6. Constantin Udrişte
    Pages 177-200
  7. Constantin Udrişte
    Pages 201-223
  8. Constantin Udrişte
    Pages 225-272
  9. Constantin Udrişte
    Pages 273-302
  10. Back Matter
    Pages 385-395

About this book

Introduction

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~te world-force law). In other words, we create a wider class of Riemann-Jacobi, Riemann-Jacobi-Lagrange, or Finsler-Jacobi manifolds, ensuring that all trajectories of a given vector field are geodesics. This is our contribution to an old open problem studied by H. Poincare, S. Sasaki and others. From the kinematic viewpoint of corpuscular intuition, a field line shows the trajectory followed by a particle at a point of the definition domain of a vector field, if the particle is sensitive to the related type of field. Therefore, field lines appear in a natural way in problems of theoretical mechanics, fluid mechanics, physics, thermodynamics, biology, chemistry, etc.

Keywords

dynamics geometry manifold mathematics mechanics

Authors and affiliations

  1. 1.Department of Mathematics and PhysicsUniversity Politehnica of BucharestBucharestRomania

Bibliographic information

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