Open AccessIntrinsic Coordinates in Practical Geodesy
Author(s) -
Marussi Antonio
Publication year - 1937
Publication title -
geophysical journal international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0956-540X
DOI - 10.1111/j.1365-246x.1937.tb07105.x
Subject(s) - figure of the earth , geodetic datum , christoffel symbols , geodesy , coordinate system , potential field , curvature , bipolar coordinates , gravitational field , displacement (psychology) , field (mathematics) , polar coordinate system , mathematics , mathematical analysis , classical mechanics , geometry , physics , generalized coordinates , geophysics , geology , pure mathematics , psychology , psychotherapist
Summary The basic ideas that support intrinsic geodesy, i. e. the discipline which aims at the local description of the gravity field of the Earth by using only coordinates and quantities that have a physical reality and that are therefore accessible to actual observation, are recalled. It is shown how the integrability conditions necessary for the existence of the coordinate surfaces, and the fundamental operators, e. g. the Christoffel symbols of the second kind connecting the principal trihedra of the intrinsic coordinate system, may be expressed in terms of the curvature parameters of the field, and of gravity. An application of the theory is made to a classical geodetic problem, i. e. the generalized expansion of Legendre for the displacement of the potential (the dynamic height) along an optical path.