Slobodan Nedic
Slobodan NEDIĆ received his Bachelor in Electrical Engineering (Electronics and Telecommunications) and MS (Signals and Information Processing) degrees from the Belgrade University, Serbia, in 1974 and 1980. He worked with the “Michael Pupin” Institute on design and deployment of voice-band modems, and continued his carrier with renowned companies as NEC (Central Research Laboratories in Kawasaki, Japan and in Princeton, New Jersey) and SiRF (CA, currently the Cambridge Silicon Radio). He has contributed to improve subchannel equalization for the FDMA/OQAM multi-carrier system. Until 2017 he has been a Senior Research Associate at the Department of PECE of the UNS FTS with main R&D interest is the OFDM/OQAM system performance enhancements. Involved in the ongoing FP7 EMPhAtiC projects, including leadership of the WP3. He has published a dozen of international conferences and journals papers, and authored/co-authored six US patents. With part of his time he has of late been devoted to critical analysis of Newtonian theories of Gravitation and Orbital Motion and following the research of a number of scientist and experimentalist directed at overcoming the shortcomings of Maxwell-ian theory and practice of electromagnetism along theoretical explanation of and foundational basis for the ‘overunity’ and/or the energy-producing “self-running” electromagnetic and mechanical systems. He is currently working on establishing correspondence between physical (aetherodynamics based) and the mathematical (set-theoretic) correspondence within general scale-invariantly structured reality – with paradigmatic reliance on multi-scaling instead of multi-dimensioning.
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Кеpler’s Equation, which relates the eccentric (and, intermediately, the true) anomaly of the planetary trajectories to the uniformly flowing time, in accordance with his Second (surface) law, in this paper are perceived with it connected certain deficiencies of the orbital mechanics and dynamics, caused by absence of the Kepler’s accompanying physical considerations, and which are repercuted in: reliance on the so-called Invariants – the First integrals of Energy and of the Angular Momentum, implicit Conservativeness, canonic formalism and omnipresence of the Symmetry principle, as well as the essential lacking of the explicit centrifugal force and its substitution by the
fictitious one. It is given а survey of the Kepler’s strivings and the results attained, as well as of his key role in the historical development of the mechanics, physics, astronomy and astrophysics, and the science in general – through insights in the branching of the science development over Newton (instead over Descartes and Leibniz), the incomplete congruence among his physical considerations
and the ultimately formulated laws, and also of the non-existent transverse acceleration ‘implied’ by the Kepler’s Second law. In support of the justification of the neglected development direction and the fundamentality of the Kepler’s insights in the need for both the attractive an repulsive interactions of the orbital and central body – the Sun, the Kepler-Ermakov second order non-linear differential equation has been reaffirmed along its adequacy for the phenomenological modeling of dynamic interactions on all the ‘scales’ in Nature: with brief reference to the “General
Aetherodynamics” of V.A. Atsukovsky, as the basis for reuse and justification of insights/results of Descartes, Leibniz, Boscovich, D’Alambert, Engels, H. Strache, M. Petrović, M. Milanković, and P, Savić. Certain implications to the Elliptic Integration, the Symplectic Integration, Symplectic Geometry/Topology, as well as the connection between physical and mathematical continua in the context of the multi-level, scale-invariant mechanics and/or dynamics - will be briefly mentioned.
Abstract in English: In this paper is given a holistic synthesis of the overall activities from fishing, over musical, ’adventuristic’ and literal, to mathematical, physical and philosophic-epistemological of Mihailo Petrovi Alas, in the context of his all-encompassing search for the unique analogue core of all the seemingly disparate phenomena. His work is viewed at as consisted of very relevant results and fruitful ideas which should contribute to fulfillment of his scientific, as well as overall-philosophic and civilizational ideal the unification of all natural and social phenomena and processes into one common physical-mathematical framework, and thus contributing to the ultimate overcoming of the traditional and untenable "compartmentalization" of the science. It is arrived at the toroidal vortex structure as the scale-invariant form, whereby the universe appears as a grand recycling of matter and movement (energy), with possibility of its substantial dynamical and mathematical-phenomenological interaction to ensure the full correspondence between the aetherodynamics-physical and the mathematics-logical continuum.
The above expression for transverse acceleration and the corresponding one for the total energy are given in the so-called “non-inertial coordinate system”, which has turned out to be rotationally-invariant to the rectangular one, so that the numerical integration in both, as well as the analytic-numerical evaluations, produce the same results corroborating the outgoing integrals. However, when evaluating in the tangential-normal generalized coordinates (numerical integration will be pursued, too) the following is realized:
1. One gets the non-zero tangential acceleration, the projection of which on the transverse direction produces non-zero transverse acceleration;
2. Integrating the gravitational force projection on tangential direction for the vertically scaled nominal ellipse with the pertinent KE, one gets the positive energy-well.
Based on this, as well as the fact that there are numerous situations where the (closed) elliptic trajectories with two central or non-central forces do not obey the area-law and Kepler’s equation, the principle of conservativeness should be reconsidered and possibly be altogether abandoned.
On the other hand, the “Kepler’s Physical Astronomy” based on his own principle that every motion has its geometrical representation while the latter has to be ‘supported’ by the truly physical processes, Kepler has very early – at the very stage of the eccentric trajectory hypothesis – realized the necessity of presence of the mechanisms of both the attraction and repulsion, through his “Physical Astronomy”, rooted on Gilbert’s book De Magnete, assigning to the Sun’s virtus-motrics causation of purely circular motion and to a Planet – vis-insitia, the intrinsic ability to modify the very circular motion. Although this has been largely unaccounted for in the subsequent development of mechanics and dynamics, it had been followed by Leibniz with his by distance’s inverse cube explicit centrifugal force, Boscovich’s intermittent attraction-repulsion Curve, (Kepler-)Ermakov’s Equation, and by this author’s extension of the Thermo-Dynamical Oscillator concept of professor VujoGordić - all this justifying Kepler’s insights.