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Differentiability and Fractality in Dynamics of Physical Systems cover
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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.

Sample Chapter(s)
Chapter 1: Principles of Motion in Invariantive Mechanics (100 KB)


Contents:
  • Principles of Motion in Invariantive Mechanics
  • Inertial Invariantive Motion of the Material Point
  • Field Invariantive Theories
  • Ondulatory Invariantive Theories. Wave-Corpuscule Duality
  • Invariantive Mechanics of Systems of Material Points
  • The Photon in Invariantive Ondulatory Theories
  • Lagrangian Approach 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 the Atom
  • Extended Fractal Hydrodynamic Model with an Arbitrary Fractal Dimension and Its Implications
  • Theory of Fractional Scale Relativity and Some Applications

Readership: Master, PhD students and professional researchers in the field of physics.