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.
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The authors succeed in that it may be considered as a fascinating book to those readers with a foot already in the door of this field. The conclusions of the authors and their relevant merits, therefore, must be left up to the experienced reader. As a well-structured presentation of ideas, however, this book successfully accomplishes its aim: the development of the dynamics of physical systems through considerations of differentiability and fractality. --Contemporary Physics
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