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Angular velocity of rotation of extended bodies in general relativity

Published online by Cambridge University Press:  25 May 2016

S.A. Klioner
S.A. Klioner*
Affiliation:
Institute of Applied Astronomy 197042 St. Petersburg, Russia

Abstract

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We consider rotational motion of an arbitrarily composed and shaped, deformable weakly self-gravitating body being a member of a system of N arbitrarily composed and shaped, deformable weakly self-gravitating bodies in the post-Newtonian approximation of general relativity. Considering importance of the notion of angular velocity of the body (Earth, pulsar) for adequate modelling of modern astronomical observations, we are aimed at introducing a post-Newtonian-accurate definition of angular velocity. Not attempting to introduce a relativistic notion of rigid body (which is well known to be ill-defined even at the first post-Newtonian approximation) we consider bodies to be deformable and introduce the post-Newtonian generalizations of the Tisserand axes and the principal axes of inertia.

Type
Part VIII - General Relativity. Physics
Information
Symposium - International Astronomical Union , Volume 172: Dynamics, Ephemerides and Astrometry of the Solar System , 1996 , pp. 309 - 320
Copyright
Copyright © Kluwer 1996 

References

Bizouard, C., Schastok, J., Soffel, M.H., Souchay, J., (1992) Étude de la rotation de la Terre dans le cadre de la relativité général: premiere approche. In: Journées 1992, Capitaine, N. (ed.), Observatoire de Paris, pp. 76–84 Google Scholar
Brumberg, V.A. (1972) Relativistic Celestial Mechanics. Nauka, Moscow. (in Russian) Google Scholar
Brumberg, V.A., Kopejkin, S.M. (1989) Relativistic Theory of Celestial Reference Frames. In Reference Frames, edited by Kovalevsky, J., Mueller, I. I. and Kołaczek, B. Kluwer Academic Publishers, pp. 115 CrossRefGoogle Scholar
Damour, T., Soffel, M., Xu, C. (1991) General Relativistic Celestial Mechanics I. Method and definition of reference systems Phys. Rev. D, Vol. no. 43, pp. 3273–3307 CrossRefGoogle ScholarPubMed
Damour, T., Soffel, M., Xu, C. (1992) General Relativistic Celestial Mechanics II. Translational Equations of Motion Phys. Rev. D, Vol. no. 45, pp. 1017–1044 CrossRefGoogle ScholarPubMed
Damour, T., Soffel, M., Xu, C. (1993) General Relativistic Celestial Mechanics III. Rotation Equations of Motion Phys. Rev. D, Vol. no. 47, pp. 3124–3137 CrossRefGoogle ScholarPubMed
Fock, V.A. (1959) Theory of space, time and gravitation. Pergamon, Oxford.Google Scholar
Klioner, S.A., Voinov, A.V. (1993) Relativistic Theory of Astronomical Reference Systems in Closed Form. Phys. Rev. D, Vol. no. 48, pp. 1451–1461 CrossRefGoogle ScholarPubMed
Kopejkin, S.M. (1988) Celestial Coordinate Reference Systems in Curved Space-Time. Celestial Mechanics, Vol. no. 44, pp. 87–115 CrossRefGoogle Scholar
Landau, L.D., Lifshitz, E.M. (1971) The Classical Theory of Fields. Pergamon Press, Oxford.Google Scholar
Moritz, H., Mueller, I.I. (1987) Earth Rotation: Theory and Observation Ungar, New York.Google Scholar
Soffel, M. (1994) The problem of rotational motion and rigid bodies in the post-Newtonian framework. unpublished notes .Google Scholar
Synge, J.L. (1960) Relativity: the General Theory. North-Holland Publishing Company, Oxford.Google Scholar
Thorne, K.S., Gürsel, Y. (1983) The free precession of slowly rotating neutron stars: rigid-body motion in general relativity, Mon. Not. R astr. Soc., Vol. no. 205, pp. 809–817 CrossRefGoogle Scholar
Voinov, A.V. (1988) Motion and rotation of celestial bodies in the post-Newtonian approximation, Celestial Mechanics, Vol. no. 41, pp. 293–307 Google Scholar