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Geometric Dynamics

  • Constantin Udrişte

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

  • Constantin Udrişte
    • 1
  1. 1.Department of Mathematics and PhysicsUniversity Politehnica of BucharestBucharestRomania

Bibliographic information

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