The rotational motion of an earth orbiting gyroscope according to the Einstein theory of general relativity

Details The rotational motion of an earth orbiting gyroscope according to the Einstein theory of general relativity The rotational motion of an earth orbiting gyroscope according to the Einstein theory of general relativity

Jul 1979

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1979cemec..20...19h&link_type=abstract

Celestial Mechanics, vol. 20, July 1979, p. 19-42.

Mathematics

1

Poisson Equation, Relativity, Rotary Gyroscopes, Satellite-Borne Instruments, Astronomical Coordinates, Equations Of Motion, Numerical Integration, Oblate Spheroids, Transformations (Mathematics)

Scientific paper

The classical Poisson equations of rotational motion are used to study the attitude motions of an earth orbiting, rapidly spinning gyroscope perturbed by the effects of general relativity (Einstein theory). The center of mass of the gyroscope is assumed to move about a rotating oblate earth in an evolving elliptic orbit which includes all first-order oblateness effects produced by the earth. A method of averaging is used to obtain a transformation of variables, for the nonresonance case, which significantly simplifies the Poisson differential equations of motion of the gyroscope. Long-term solutions are obtained by an exact analytical integration of the simplified transformed equations. These solutions may be used to predict both the orientation of the gyroscope and the motion of its rotational angular momentum vector as viewed from its center of mass. The results are valid for all eccentricities and all inclinations not near the critical inclination.

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