Differentiability And Fractality In Dynamics Of Physical Systems

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 MechanicsInertial Invariantive Motion of the Material PointField Invariantive TheoriesOndulatory Invariantive Theories. Wave-Corpuscule DualityInvariantive Mechanics of Systems of Material PointsThe Photon in Invariantive Ondulatory TheoriesLagrangian Approach in Invariantive MechanicsConsiderations on Invariantive MechanicsInvariantive Mechanics of Rigid BodyCovariant Formulation of Conservation Laws in Invariantive MechanicsInvariantive Mechanics and Informational EnergyChaos Via Fractality in Gravitational Dynamical SystemsFractality at Small Scale. Fractal Model of the AtomExtended Fractal Hydrodynamic Model with an Arbitrary Fractal Dimension and Its ImplicationsTheory of Fractional Scale Relativity and Some Applications
Readership: Master, PhD students and professional researchers in the field of physics.
Key Features:Theory of 1-forms is applied to dynamics of material points systemsNon-differentiability as a possible property of complex systemsThe role played by informational energy in the definition of the constants of motion is discussed