| 書目名稱 | Geometric Dynamics | | 編輯 | Constantin Udri?te | | 視頻video | http://file.papertrans.cn/384/383506/383506.mp4 | | 叢書名稱 | Mathematics and Its Applications | | 圖書封面 |  | | 描述 | 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 | | 出版日期 | Book 2000 | | 關(guān)鍵詞 | dynamics; geometry; manifold; mathematics; mechanics | | 版次 | 1 | | doi | https://doi.org/10.1007/978-94-011-4187-1 | | isbn_softcover | 978-94-010-5822-3 | | isbn_ebook | 978-94-011-4187-1 | | copyright | Kluwer Academic Publishers 2000 |
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