Geodesic
On the Somigliana's formula
Applications of Mathematics, Tome 16 (1971) no. 2, pp. 98-108
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This paper deals with the general derivation of Pizzetti-Somigliana's formula for the decomposition of gravity. The problem of derivation is solved formally geometrically on the equipotential surface $S$ that need not be the oblate ellipsoid of rotation. In individual cases of confocal systems of quadrics, the introduction of hyperbolic and circular functions in the equations of tri-orthogonal system is motivated. It is indicated that the validity of the formula may be formally generalized also to other quadrics of rotation.
This paper deals with the general derivation of Pizzetti-Somigliana's formula for the decomposition of gravity. The problem of derivation is solved formally geometrically on the equipotential surface $S$ that need not be the oblate ellipsoid of rotation. In individual cases of confocal systems of quadrics, the introduction of hyperbolic and circular functions in the equations of tri-orthogonal system is motivated. It is indicated that the validity of the formula may be formally generalized also to other quadrics of rotation. 
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Hora, Ladislav. On the Somigliana's formula. Applications of Mathematics, Tome 16 (1971) no. 2, pp. 98-108. doi: 10.21136/AM.1971.103334

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