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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.
