Open AccessNonlinear Mechanics in Seismometry Problems
Author(s) -
Ullmann W.
Publication year - 1966
Publication title -
geophysical journal of the royal astronomical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0016-8009
DOI - 10.1111/j.1365-246x.1966.tb03499.x
Subject(s) - interpretation (philosophy) , tensor (intrinsic definition) , nonlinear system , metric (unit) , metric tensor , set (abstract data type) , mathematics , differential geometry , theoretical physics , classical mechanics , computer science , mathematical analysis , geometry , physics , quantum mechanics , operations management , geodesic , economics , programming language
Summary A seismic apparatus can as well be understood as mechanism, if electromagnetic fields are part of the physical—technical system. Electrical‐mechanical analogies make possible the mechanical interpretation of the holonomous system taken into consideration. The general theory suggests the introduction of an f ‐dimensional elementary set to whose points the f generalized coordinates of the mechanism can be assigned. This set is a Riemannian space whose metric is defined by the choice of the energy tensor for the metric tensor. The presumed model proves to be very instructive, because the differential‐geometric interpretation of the structure of the mechanism is clear and within a far‐reaching reliable mathematical theory. The‘Euclidian structure’of the seismic apparatus is marked by especially clear qualities. More complicated structures can be classified by differential‐geometric points of view. Such a classification is also useful for the integration theory.