| Geometric Dynamics Softcover Repri Edition Contributor(s): Udriste, C. (Author) |
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ISBN: 9401058229 ISBN-13: 9789401058223 Publisher: Springer OUR PRICE: $52.24 Product Type: Paperback Published: October 2012 |
| Additional Information |
| BISAC Categories: - Mathematics | Vector Analysis - Medical - Mathematics | Applied |
| Dewey: 515.63 |
| Series: Mathematics and Its Applications |
| Physical Information: 0.85" H x 6.14" W x 9.21" (1.28 lbs) 395 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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. |