Geometric Dynamics: 513 (Mathematics and Its Applications, 513) - Softcover

Udriste, C.

Softcover

ISBN 10: 9401058229 ISBN 13: 9789401058223

Publisher: Springer, 2012

Synopsis

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.

Edition details

• Publisher: Springer
• Publication date: 2012
• Language: English
• ISBN 10: 9401058229
• ISBN 13: 9789401058223
• Binding: Paperback
• Number of pages: 411