Ueber die Fortpflanzung ebener Luftwellen von endlicher Schwingungsweite. Offprint from: Abhandlungen der Koniglichen Gesselschaft der Wissenschaften zu Gottingen, Bd. 8. THE MATHEMATICS OF SHOCK WAVES. FORMERLY OWNED BY WERNHER VON BRAUN'S PROFESSOR

RIEMANN, Georg Friedrich Bernhard

Published by Gottingen: Dieterich, 1860

About this Item

First edition, very rare separately-paginated offprint (journal pagination 43-65), and with a distinguished provenance, of Riemann's "most important contribution to mathematical physics" (DSB). This work inaugurated the study of shock waves, and made important advances in the theory of partial differential equations. "Riemann's most important contribution to mathematical physics was his 1860 paper on sound waves. Sound waves of infinitesimal amplitude were well known; Riemann studied those of finite amplitude in the one-dimensional case and under the assumption that the pressure p depended on the density in a definite way. Riemann's presentation discloses so strong an intuitive motivation that the reader feels inclined to illustrate every step of the mathematical presentation by a drawing . . . [He shows that] an original disturbance splits into two opposite waves. Since phases with large p travel faster, they should overtake their predecessors. Actually the rarefaction waves grow thicker, and the condensation waves thinner finally becoming shock waves . . . Riemann's paper on sound waves is also very important mathematically, giving rise to the general theory of hyperbolic differential equations. Riemann introduced the adjoint equation and translated Green's function from the elliptic to the hyperbolic case where it is usually called Riemann's function" (DSB). Riemann begins his paper as follows (translation from Laugwitz, Bernhard Riemann 1826-1866. Turning Ponts in the Conception of Mathematics (1999), p. 264): "This investigation does not claim to provide useful results for experimental research; the author would like it to be regarded as just a contribution to the theory of nonlinear partial differential equations. Just as the most fruitful methods for the integration of linear partial differential equations have been obtained not by developing the general idea of this problem but rather by treating particular physical problems, so too the theory of nonlinear partial differential equations seems to be best advanced by a circumstantial treatment of particular physical problems which takes into consideration all constraints. In fact, the solution of the very special problem that is the subject of this paper has yielded new methods and approaches that will probably also play a role in more general problems." Provenance: Joseph Ackeret (1898-1981), Swiss aeronautical engineer widely viewed as one of the foremost aeronautics experts of the 20th century (ink stamp on title). From 1921 to 1927 he worked with Ludwig Prandtl at the "Aerodynamische Versuchsanstalt" in Göttingen, later becoming a professor of Aerodynamics at ETH Zurich in 1931, where Wernher von Braun was one of his students. OCLC records only one copy in the US, at the Smithsonian. 4to, pp. 25. Green paper spine strip as issued. Very good. Seller Inventory # ABE-1505830058438

Bibliographic Details

Title: Ueber die Fortpflanzung ebener Luftwellen ...

Publisher: Gottingen: Dieterich

Publication Date: 1860

Binding: No Binding

Condition: Very Good

Edition: 1st Edition