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Abstract

Im Rahmen des analytischen Formalismus der Mechanik von Hertz wird eine mathematische Fassung der „teleskopischen” Prinzipien der Dynamik angegeben, welche die „Relativität der Trägheit” gemäß Huygens und Mach, die allgemeine Galileische „Reziprozität der Bewegungen” und die Mach-Einstein-Doktrin der Vollständigen Induktion der Trägheit durch die Gravitation enthält. - Den Anschluß dieser „trägheitsfreien Gravodynamik” im Hertzschen „Konfigurationsraum des Universums” V3N and Einsteins ART geben die kosmologischen Prinzipien von Mach und Einstein. Der Einstein-Kosmos definiert über die Normierung |Φ| = c2/3 des kosmischen Gravitationspotentials Φ die relativistische Fundamentalgeschwindigkeit c auch für eine Galileiinvariante Dynamik. Auf diesen Einstein-Kosmos bezogen, ergibt unsere Gravodynamik als lokale Himmelsmechanik die Newtonsche Gravitationstheorie mit den Einsteinschen „nach-Newtonschen” Korrekturen.

Machs Prinzip oder die Mach-Einstein-Doktrin sind also keineswegs bloße „philosophische Postulate,” sondern analytische Bedingungen an die Prinzipe der Mechanik. Sie stellen anholonome Verknüpfungen zwischen den Massenpunkten der Hertzschen Mechanik dar.

The Telescopical Principles in the Theory of Gravitation. (Machs Principle, Relativity of Inertia According to Mach and Einstein and Hertz' Mechanics)

We give an explication and analytical formulation of Mach's principle of the “relativity of inertia” and of the Mach-Einstein doctrine on the determination of inertia by gravitation. These principles are whether “philosophical” nor “epistemological” postulates but well defined physical axioms with exactly analytical expressions. - The fundamental principle is the Galileian “reciprocity of motions”. According to this “generalized Galilei invariance” the principal functions of analytical dynamics (Lagrangian L and Hamiltonian H) are depending upon the differences ��AB of the coordinate vectors ��A and ��B of the velocity differences ��AB = ��A-��B, only. The Galileian reciprocity of motions means that whether the vectors ��A and ��A nor the accelerations ��A of one particle have a physical significance.

A mechanics obtaining this generalized Gailei-invariance cannot depend upon a kinematical Term equation image in the Lagrangian. Therefore, the inertial masses of the particles must be homogeneous function of interaction potentials ΦA,B. According to the Einsteinian equivalence of inertia and gravity these interactions have to be the Newtonian gravitation.

In a universe with N mass points the Mach-Einsteinian Lagrangian for our “gravodynamics without inertia” is

chemical structure image

In such a Mach-Einstein universe the celestical dynamics becomes in the first approximation the Newtonian dynamics, in the second (the “post-Newtonian”) approximation the general relativistic Einstein effects are resulting.-However, our gravodynamics gives new effects for large masses (no gravitational collapses) and in cosmology (secular accelerations a.o.).

Generally, the space of our gravodynamics is whether the Newtonian “absolute space” V3 nor the relativistic Einstein-Minkowski world V4 but the Hertzian configuration space V3N of the N particles. According to the relativity of inertia the Hertzian metrics become Riemannian metrics which are homogenous functions of the Newtonian gravitational potentials.

chemical structure image.