Differentiability and Fractality in Dynamics of Physical Systems

Merches, Ioan/ Agop, Maricel

World Scientific Publishing Co Pte Ltd（2015/10発売）

• 製本 Hardcover:ハードカバー版／ページ数 300 p.
• 言語 ENG
• 商品コード 9789814678384
• DDC分類 515.39

Full Description

Using Cartan's differential 1-forms theory, and assuming that the motion variables depend on Euclidean invariants, certain dynamics of the material point and systems of material points are developed. Within such a frame, the Newtonian force as mass inertial interaction at the intragalactic scale, and the Hubble-type repulsive interaction at intergalactic distances, are developed.The wave-corpuscle duality implies movements on curves of constant informational energy, which implies both quantizations and dynamics of velocity limits.Analysis of motion of a charged particle in a combined field which is electromagnetic and with constant magnetism implies fractal trajectories. Mechanics of material points in a fractalic space is constructed, and various applications — fractal atom, potential well, free particle, etc. — are discussed.

Contents

Principles of Motion in Invariantive Mechanics; Inertial Invariantive Motion of the Material Point; Field Invariantive Theories; Ondulator Invariantive Theories. Wave-Corpuscule Duality; Invariantive Mechanics of Systems of Material Points; The Photon in Invariantive Ondulator Theories; Lagrangian Method in Invariantive Mechanics; Considerations on Invariantive Mechanics; Invariantive Mechanics of Rigid Body; Covariant Formulation of Conservation Laws in Invariantive Mechanics; Invariantive Mechanics and Informational Energy; Chaos via Fractality in Gravitational Dynamical Systems; Fractality at Small Scale. Fractal Model of Atom; Extended Fractal Hydrodynamic Model with an Arbitrary Fractal Dimension and Its Implications; Theory of Fractional Scale Relativity and Some Applications;