KPHTHKA

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REVIEWS

GPS-Techniques A p p l i e d t o G e o d e s y a n d S u r v e y i n g . E. Groten, R. Strauss (Eds.). Lectures Notes in E a r t h Sciences, Vol. 19, Springer-Vlg., Berlin--Heidelberg, 1988. XVtI, 532 pp., 162 figs., 88 tabs., soft cover. The book contains proceedings of the International GPS-Workshop held in Darmstadt, F.R.G., April 10 to 13, 1988 under the auspices o f the International Association of Geodesy. The instalation of the Global Positioning System (GPS) started a b o u t 15 years ago and its potential possibilities are going to influence the development of geodesy significantly, although the final result of the presently occurring collision between classical and modern concepts is not k n o w n yet. In the volume the reader will find a collection of 44 papers which were presented during 9 sessions of the Workshop. In addition, he will certainly appreciate the publication of the opening and welcome addresses, of a brief summary of the panel discussion, of the full text of 6 resolutions adopted at the Workshop and, finally, o f the appendix with results o f field measurements dem o n s t r a t e d by various GPS-manufacturers during the Workshop. These parts complete a representative and fascinating picture given by the volume on the development of GPS-technology and its applications which have become surprisingly efficient and effective in a short time. The first section of the volume contains 4 contributions devoted to general aspects such as problems of a centimeter-level accuracy in GPS-measurements, relativistic effects in GPS, global cooperation and goals, etc. The second section contains 5 contributions and discusses applications of GPS in geodesy, geodynamics, engineering and improvements of the conventional terrestrial coordinate system. The third a n d fourth sections contain a t o t a l of 11 contributions devoted to GPS-campaings and instrumerAs. The reader will find results of national and international GPS-trackings, comparisons with classical control networks and laser and VLBI observations. Some contributions deal with simulation and modelling problems, with system and hardware oriented aspects, etc. The fifth and sixth sections contain a t o t a l of 9 contributions and discuss kinematic applications of GPS. Here the GPS-static and kinematic survey modes are compared. Technical and software problems in the GPS-kinematic mode are discussed as well as its field of application in surveying a n d navigation, and its potential possibilities to achieve a relatively short occupation time necessary at each survey mark. The seventh section contains 4 contributions and it is specially devoted to problems of software development including the GPS-carrier phases and clock modelling, cycle-slip detection and carrier phase ambiguity resolution. The papers discuss data processing techniques and strategies necessary to obtain the highest possible accuracies. The eighth section contains 5 contributions treatieg the use of GPS in geodynamics. In particular they discuss the GPS-experiments in Iceland, the Central A n d e a n GPS-traverse, monitoring tectonic plate m o t i o n and recovering Earth's r o t a t i o n parameters with GPS. The ninth section contains 6 papers dealing with some special applications and orbits. Attention is paid to the European Tracking Network, to the World Geodetic System 1984, to the solar radiation pressure and to adjustment systems for multistation positioning and orbit determination. Although the b o o k is a collection of papers presented by various authors from 14 nations during the Workshop, it brings a broad and comprehensive review of the prezent state of the art and research activities in GPS-technology and its agplications. Undoubtedly this result is a success o f the organizers of the Workshop who provided a number of international experts with scope to cover the individual topics in the field of GPS-methods. The b o o k meets high standards o f quick publications on new developments in research and technology. Its usefulness is enhanced by a n u m b e r of illustrations, graphs and figures. It is indeed necessary to realize that GPS represents an i m p o r t a n t concept in modern satellite and space methods. GPS-procedures are still at their beginning and the full spectrum of their capabilities still has to be explored. The book is addressed to a large and still growing c o m m u n i t y o f users o f GPS-methods as well as to researchers in this field with a promising future. In conclusion, we can state that the b o o k is a very valuable source of i n f o r m a t i o n which can be o f very 78

Studla geoph, et geod. 34 (1990},

Reviews good service to everyone, but especially to geodesists, interested in basic research as well as practical applications in this modern field. Petr Holota

S i e g f r i e d H e i t z : Coordinates in Geodesy. Springer-Verlag Berlin, Heidelberg, New York, London, Paris, Tokyo, 1988. XII and 255 pages, 20 figures. D M 5 8 , - - . Original German edition: Koordinaten auf geod~tisehen Bezugsfl/ichen. Ferd. DfimmlersVerlag, Bonn 1985. The revised English version differs from the German in two parts, mainly in the passage in Chapter 3 about the inversion o f power series and particularly in the whole of Chapter 5 about geodetically significant coordinate systems in three-dimensional Euclidean space. The book is an excellent contribution to the geodetic literature where it has an exceptional position. It contains applications o f differential geometry to the study o f geodetic coordinate sy.~;tems and to the transformations between them. The b o o k has two great advantages: 1. It is not limited only to the reference ellipsoid, but it works with general surfaces; 2. It consequently uses methods o f the tensor calculus. Ad I.: The idea that studies only on the ellipsoid o f revolution lead to simplification is not correct. This concept is lent stro~?g support in the 1st volume of Helmert's classical work. The mathematician acquainted with Helmert's book cannot omit that the drawn out calculations due to the choice o f a spceial surface (e.g. the ellipsoid o f revolution) often obscure the geometrical content which stands out clearly only if one treats the matter on a general surface. Ad 2.: Differential geometry can also be studied without using a special method. It can even seem that one is saving the time necessary to master that method. But the tensor calculus is a very powerful tool which gives us an uniform it:sight ir~to the studied problems and which provides the basis for studying curved multidimensional spaces which geodesy will also e~.eounter in the future. After the sthort introductory Chapter 1 (pp. 1-- 9), Chapter 2 (General Fundamentals o f Surface Coordinates, pp. 10--68) is devoted, in relatively great detail, to differential geometry o f sm faces and contains an appendix dealing with the fLmctions of a complex variable. Chapter 3 (Representing the Transformation Equations Between Surface Coordinates by Power Series, pp. 69--98) following the above mentioned appendix, applies the infinite series to the study o f geodetic triangles and especially to geodetic or isothermal coordinate systems. Chapter 4 (Surface Coordinates on Ellipsoides of Revolution, pp. 99--- t65), studies the special coordi~aate systems on a reference surface and the transformations between them; emphasis is again put o~a isothermal coordinates. Chapter 5 (Three-Dimensional Coordinates, pp. 166--241) begins with the study o f curvilinear coordinates in three-dimensional space, which is followed by the ir~vestigation o f coordinate systems significant for geodesy and the transformations between them. - - The book ends with a bibliography (divided into mathematical foundations and geodetic applications) and an index. The reviewer would also like to add some comments from the point of view of his profession The major-part o f Chapter 2 is devoted to the tensor concept of differential geometry. U n d e r standing this part is a prerequisite to the further use o f this book. F r o m my lectures for geodesists based on the book by M. Hotine: Mathematical Geodesy, I am aware that the simultaneous study of the geometrical content and the method o f tensor calculus is not an easy matter. That is why the book will be easy to read for those who are acquainted with the traditional concept o f differential geometry and its geodetic applications - - possibly to the extent o f the first half o f F. I-Iopfner's book (1948) -- and who will thus be able to concentrate on the method of tensor calculus. These readers will also be able to recognize very distinctly the advantages o f tensor calculus.

Studia geoph, et geod, 34 (1990)

79

Reviews T h e Danish geodesist Caspar Wessel (1745--1818) was the first to introduce the geometric representation of complex numbers (par. 2.2.2 and fig. 2.7). His paper published in 1799 fell futly into oblivion and was n o t found until a h u n d r e d years later, when the term " G a u s s plane" h a d already become quite common. The theory of convex sets meanwhile stays a p a r t from geodesy. The geodetic function W (p. 101) is related simply to the support functions o f an ellipse: h(B)----- a W(B). The radius of the curvature of a curve with the support function h(B) is expressed by Minkowski's formula: h(B) + d2(B)/dB 2. Analogously Weingarten's formula - - with Beltrami's second differential operator instead of the second derivative -- expresses sum of the radii of the normal curvatures of a surface by means of its support function. The definition of the surface-normal coordinates o n p. 181 deserves some attention, too, for the reason of treating with a general surface. Six normals can b e drawn to the reference triaxial ellipsoid from a point (some o f t h e m can coincide or can be imaginary); it is, o f course, clear which of them to choose, b u t it would be better to spell it out. This situation occurs if the local or global study is to be emphasized. The problem o f drawing normals to a quadric surface from a point is very interesting from the geometrical (mathematical) point of view, too, and still presents open questions. A further connection with geometry arises in the definition of surfacenormal coordinates: The normals to a surface from a two-parametric system which has been studied frequently in the theory of line congruences. The geodetic and the geometric problems are quite identical here. The present b o o k has a predecessor, as to the geodetic applications of the tensor calculus, in the b o o k by M. Hotine: Mathematical Geodesy, 1969, which the a u t h o r quotes in the bibliography (in the part Mathematical Fundamentals). The fact t h a t tensor calculus has a great significant counterpart in C a r t a n ' s calculus of exterior forms, especially with Darboux's m e t h o d o f the moving frame, should also be mentioned. The reviewer, n o t a geodesist by profession, appreciates the b o o k as a very significant and successful step towards new ways o f forming the connection between geodesy and geometry a n d wishes the possibly greatest merited success to the book.

Zbyndk Nddenik

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Studla geoph, et geod. 34 (t990)