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Anholonomity in Pre-and Relativistic Geodesy

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Relativistic Geodesy

Part of the book series: Fundamental Theories of Physics ((FTPH,volume 196))

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Abstract

I was invited to speak about anholonomity or the problem to find coordinate reference systems which are differentiable. In general non-differentiable functions like (pseudo) orthonormal reference systems are differentiable forms being not classical functions. These differentiable forms are the basis of Elie Cartan’s “exterior calculus”. Geodetic examples are extensively reviewed in the context of the pre-and relativistic Geodesy.

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Acknowledgements

C. Lämmerzahl and D. Pützfeld, /Bremen/ invited me to speak about anholonomity in the context of Relativistic Geodesy within the WE-Heraeus Seminar. Special thanks go to D. Pützfeld, F.W. Hehl/Cologne/ and H. Quevedo/Mexico City/ for their helpful comments. In addition, I am grateful for the support of J. Müller (Hanover) on the International Reference Ellipsoid and to S. M. Kopeikin (Columbia/Missouri) on studying Relativistic Equilibrium Figures and the relativistic theory of the Geoid. Last, but not least, I am grateful to M.A. Javaid(Stuttgart) for his expert typing.

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  1. Department of Geodesy and Geoinformatics, Faculty of Aerospace Engineering and Geodesy, Faculty of Mathematics and Physics, Geschwister Scholl Strasse 24 D, 70174, Stuttgart, Germany

    Erik W. Grafarend

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  1. ZARM, University of Bremen, Bremen, Germany

    Dirk Puetzfeld

  2. ZARM, University of Bremen, Bremen, Germany

    Claus Lämmerzahl

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Grafarend, E.W. (2019). Anholonomity in Pre-and Relativistic Geodesy. In: Puetzfeld, D., Lämmerzahl, C. (eds) Relativistic Geodesy. Fundamental Theories of Physics, vol 196. Springer, Cham. https://doi.org/10.1007/978-3-030-11500-5_7

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