Historischer Überblick zur mathematischen Theorie von Unstetigkeitswellen seit Riemann und Christoffel

1981

We give a brief historical account of the development of the mathematical theory of propagation of discontinuities in gases, fluids or elastic materials. The theory was initiated by Riemann who investigated the propagation of shocks in one-dimensional isentropic gas flow. Riemann’s results were used by Christoffel to treat, more generally, the propagation of (first order) discontinuity surfaces in three-dimensional flows of perfect fluids. Subsequently Christoffel applied his general theory to first order waves in certain elastic materials. Independently of Riemann and Christoffel significant contributions were made by Hugoniot. The theory was completed in Hadamard’s celebrated monograph [3…

Navigationsformel zu A. Busemanns Variationsproblem der Raumfahrt

1970

Die Indikatrix des Variationsproblems wird auser durch die Storungsdifferentialgleichung fur die grose Halbachse und die Exzentrizitat durch einen Zusammenhang zwischen der Richtung des Impulsausstoses und der exzentrischen Anomalie gegeben. Die Hamilton-Gleichungen einer Extremalen reduzieren sich dann auf eine Navigationsgleichung. Die restlichen Storungsgleichungen fur die Perihellange und die mittlere Lange der Epoche geben schlieslich den sparsamsten zeitlichen Ablauf des Raketenausstoses.

Approximation von extremalflächenstücken (hyperbolischen typs) durch charakteristische räumliche vierecke

1982

We consider solutions z of the Cauchy-problem for hyperbolic Euler-Lagrange equations derived from a general Lagrangian f(x, y, z; zx, zy) in two independent variables x, y. z is supposed to be an extremal of the corresponding variational problem. Visualizing z as a surface in R3 we give a geometric interpretation of Lewy's well-known characteristic approximation scheme for the numerical solution of second order hyperbolic equations by approximating z via a polyhedral construction built up from subunits which consist of two characteristic triangles having one side in common but lying on different planes in R3. Utilizing ideas from Cartan-geometry one can (in an appropriate sense) introduce …

G. Herglotz’ Behandlung von Beschleunigungswellen in seiner Vorlesung «Mechanik der Kontinua» angewandt auf die Stosswellen von Christoffel

1981

Following a lecture delivered by Herglotz in 1925/26 we briefly treat acceleration waves in hyperelastic materials. Our main result is a divergence equation for the squared Euclidean norm of the so-called ‘wave vector’. We then apply Herglotz’ method (devised for acceleration waves) to the propagation of such first order discontinuities in elastic bodies as were treated by Christoffel in [1].

Feynman-diagramme als vektorsysteme invariantentheoretisch behandelt (compton-streuung, elektron-positron-vernichtung

1985

Employing a special contact transformation devised by S. Lie, which takes spheres into lines, we interpret the Feynman diagrams of photon electron scattering in terms of vector systems. This gives a nice kinematic model of Compton scattering. We further compute in detail the transition probabilities of the Compton scattering process by making use of the calculus of chains of complexes from classical invariant theory rather than applying the usual Dirac-matrix technique. In the final paragraph of this paper an application of our calculations to the treatment of myon decay is indicated.

Extremale geschlossene Differentialformen Unterschallstr�mungen im Gro�en

1959