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Post-Newtonian treatise on the rotational motion of a finite body

Published online by Cambridge University Press:  04 August 2017

T. Fukushima
T. Fukushima*
Affiliation:
Geodesy and Geophysics Division, Hydrographic Department, 3-1, Tsukiji 5-chome, Chuo-ku, Tokyo 104, Japan

Abstract

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The definition of the angular momentum of a finite body is given in the post-Newtonian framework. The non-rotating and the rigidly rotating proper reference frame(PRF)s attached to the body are introduced as the basic coordinate systems. The rigid body in the post-Newtonian framework is defined as the body resting in a rigidly rotating PRF of the body. The feasibility of this rigidity is assured by assuming suitable functional forms of the density and the stress tensor of the body. The evaluation of the time variation of the angular momentum in the above two coordinate systems leads to the post-Newtonian Euler's equation of motion of a rigid body. The distinctive feature of this equation is that both the moment of inertia and the torque are functions of the angular velocity and the angular acceleration. The obtained equation is solved for a homogeneous spheroid suffering no torque. The post-Newtonian correction to the Newtonian free precession is a linear combination of the second, fourth and sixth harmonics of the precessional frequency. The relative magnitude of the correction is so small as of order of 10−23 in the case of the Earth.

Type
Dynamical Effects in General Relativity
Information
Symposium - International Astronomical Union , Volume 114: Relativity in Celestial Mechanics and Astrometry , 1986 , pp. 35 - 40
Copyright
Copyright © Reidel 1986 

References

Goldstein, H.: 1980, Classical mechanics, 2nd ed., Addison-Wesley Publ. Co. Inc., Reading, Mass. Google Scholar
Fukushima, T., Fujimoto, M.-K., Kinoshita, H., and Aoki, S.: 1986, ‘Coordinate systems in the general relativistic framework’, Proceedings of IAU Symp, No. 114 held at Leningrad, May, 1985, D. Reidel Publ. Co., Dordrecht, Holland.Google Scholar
Misner, C.W., Thorne, K.S., and Wheeler, J.A.: 1970, Gravitation, W.H. Freeman and Co., San Francisco.Google Scholar
Will, C.M.: 1981, Theory and experiment in gravitational physics, Cambridge Univ. Press, Cambridge.Google Scholar