122589785
Models for Constrained Motion and d'Alembert's Principle
A theorem of Arnol'd and Gallavotti states that by a suitable potential of increasing rigidity a mechanical system with conservative forces can be constrained to a hypersurface of the configuration space and its motion approaches a solution of the reduced Lagrangian equation. In this paper the theorem will be generalized to time- and velocity-dependent forces including time-dependent constraints and proved with the aid of the method of averaging. This technique also allows us to identify the constraint force as the averaged negative gradient of the constraint potential.
117822141
Axiomatic Characterization of Physical Geometry
Operations with rigid bodies.- Regions and transport mappings.- The Helmhotz-Lie problem.- Characterization of Euclidean geometry.
123288737
On Static Asymptotically Flat Solutions of Fourth Order Gravitational Field Equations
It is shown that each non-flat regular static asymptotically flat solution of the gravitational field equation following from the Lagrangian 
 
 
 
 
 
 
has in a certain sense positive energy. Further, for a set of parameters including the BACH-EINSTEIN theory 
 
 
 
 
 
 
some results concerning the full nonlinear behaviour of the solutions of the field equation will be given. 
 
 
 
Uber statisch asymptotisch flache Losungen von Gravitationsfeldgleichungen vierter Ordnung 
 
 
 
Es wird gezeigt, das jede nicht-flache regulare statische asymptotisch flache Losung der Gravitationsfeldgleichung, die aus einem Lagrangeausdruck 
 
 
 
 
 
 
folgt, in einem gewissen Sinne positive Energie hat. Ferner wird fur eine bestimmte Parametermenge, die die BACH-EINSTEIN-Theorie 
 
 
 
 
 
 
enthalt, einiges uber das volle nichtlineare Verhalten der Losungen der Feldgleichung mitgeteilt.
14074913
4D wormhole with signature change in the presence of extra dimensions
A regular vacuum solution in 5D gravity on the principal bundle with the U(1) structural group is proposed as a 4D wormhole. This solution has two null hypersurfaces where an interchange of the sign of some 5D metric components happens. For a 4D observer living on the base of this principal bundle this is a wormhole with two asymptotically flat Lorentzian (Euclidean) spacetimes connected by a Euclidean (Lorentzian) throat. The 4D Lorentzian observer sees these two null hypersurfaces as electric charges.
17350104
Inhomogeneous Cosmological Models with Flat Slices Generated from the EINSTEIN‐DE SITTER Universe
A family of cosmological models in considered which in a certain synchronized system of reference possess flat slices t = const. They are generated from the EINSTEIN-DE SITTER universe by a suitable transformation. Under physically reasonable presumptions these transformed models fulfil certain energy conditions. 
 
 
 
Es wird eine Familie kosmologischer Modelle betrachtet, die in einemi gewissen synchronisierten Bezugssystem flache Schichten t = const. besitzen. Sie werden mittels einer geeigneten Transformation aus dem EINSTEIN-DE SITTER-Universum erzeugt. Diese transformierten Modelle erfullen unter physikalisch sinnvollen Voraussetzungen gewisse Energie bedingungen.