The Reference Frames and a Transformation of the Spherical Functions

Abstract

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.