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The Reference Frames and a Transformation of the Spherical Functions

Published online by Cambridge University Press:  12 April 2016

V. G. Shkodrov
V. G. Shkodrov*
Affiliation:
Section of Astronomy Bulgarian Academy of SciencesSofia, Bulgaria

Abstract

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The use of spherical functions in dynamical problems is very common. As a rule, they arise in perturbing functions. It is well known that passing from one reference frame to another is accompanied by a double transformation of the perturbation function. That is why problems lose their simplicity and elegance. The problem of two solid bodies is a typical example in this respect.

In the present paper the questions connected with the transformation of the spherical functions when passing from one reference frame to another frame are considered. Traditional functions are generally unsuitable as they introduce a series of difficulties in the problems. That is why complex spherical functions are used. The transformation of spherical functions due to rotation of the coordinate frame is made by means of the Wigner’s functions. When translating the frame the Clebsch-Gordon’s coefficients are used.

Type
Research Article
Information
International Astronomical Union Colloquium , Volume 56: Reference Coordinate Systems for Earth Dynamics , August 1980 , pp. 255 - 259
Copyright
Copyright © Reidel 1981

References

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