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 ...
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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.
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Add this copy of Geometric Dynamics to cart. $51.65, new condition, Sold by Ingram Customer Returns Center rated 5.0 out of 5 stars, ships from NV, USA, published 2012 by Springer.
Add this copy of Geometric Dynamics to cart. $62.20, new condition, Sold by Ria Christie Books rated 5.0 out of 5 stars, ships from Uxbridge, MIDDLESEX, UNITED KINGDOM.
Add this copy of Geometric Dynamics to cart. $68.59, new condition, Sold by Ria Christie Books rated 5.0 out of 5 stars, ships from Uxbridge, MIDDLESEX, UNITED KINGDOM, published 2012 by Springer.
