Geometric Dynamics (Paperback, Softcover reprint of the original 1st ed. 2000)

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.

General

Imprint:	Springer
Country of origin:	Netherlands
Series:	Mathematics and Its Applications, 513
Release date:	October 2012
First published:	2000
Authors:	C. Udriste
Dimensions:	240 x 160 x 22mm (L x W x T)
Format:	Paperback
Pages:	395
Edition:	Softcover reprint of the original 1st ed. 2000
ISBN-13:	978-9401058223
Categories:	Books > Science & Mathematics > Mathematics > Numerical analysis Books > Science & Mathematics > Mathematics > Geometry > Differential & Riemannian geometry Books > Science & Mathematics > Mathematics > Optimization > General Books > Science & Mathematics > Mathematics > Applied mathematics > Mathematical modelling Promotions
LSN:	9401058229
Barcode:	9789401058223

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