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Дата последнего поиска статьи во внешних источниках: 11 ноября 2019 г.
Аннотация:Abstract— A problem of mutual potential energy of two elliptical gravitating (or electrostatically charged)Gaussian rings is formulated and solved. Coplanar rings have apse lines that generally make an angle with each other. The mutual energy of the rings is found in quadratic approximation with respect to ring eccentricities e and e . At the first stage, the potential of the Gaussian ring is represented as a series in terms of
1 2
eccentricity and determined at the points of another elliptical ring (note theoretical importance of such a result). Linear (with respect to quantities e and e ) terms are absent in the expression for the mutual energy 1 2
2 2
of the rings, and the coefficients of the second-order terms (e1 and e2 ) are equal to each other. Only one coefficient of mixed term (e e ) is determined by the tilt angle of the apse lines. Such a result can be used to easily 1 2
determine the moment of force between the rings that is needed for the study of small mutual rotational oscil-
lations of the Gaussian rings.