| Title:
|
On the Somigliana's formula (English) |
| Author:
|
Hora, Ladislav |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
16 |
| Issue:
|
2 |
| Year:
|
1971 |
| Pages:
|
98-108 |
| Summary lang:
|
English |
| Summary lang:
|
Czech |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. () |
| DOI:
|
10.21136/AM.1971.103334 |
| . |
| Date available:
|
2008-05-20T17:50:05Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/103334 |
| . |
| Reference:
|
[1] C. F. Baeschlin: Lehrbuch der Geodäsie.Zürich 1948. Zbl 0040.38701 |
| Reference:
|
[2] H. П. Грушинский: Теория фигуры земли.Москва 1968. Zbl 1171.62301 |
| Reference:
|
[3] W. A. Heiskanen H. Moritz: Physical Geodesy.San Francisco and London 1967. |
| Reference:
|
[4] V. Hlavatý: Diferenciální geometrie křivek a ploch.Praha 1937. |
| Reference:
|
[5] E. Kamke: Differentialgleichungen, Lösungsmethoden und Lösungen.Leipzig 1956. Zbl 0073.07802 |
| Reference:
|
[6] J. Lense: Kugelfunktionen.Leipzig 1950. Zbl 0038.22202, MR 0040486 |
| Reference:
|
[7] M. С. Молоденский В. Ф. Еремеев M. И. Юркина: Методы изучения внешнего гравитационного поля и фигуры земли.Tp. ЦНИИГАиК, вып. 131, Москва 1960. Zbl 1225.94001 |
| Reference:
|
[8] P. Pizzetti: Principi della teoria meccanica della figura dei pieneti.Pisa 1913. |
| Reference:
|
[9] С. Somigliana: Teoria generale del campo gravitazionale dell'ellissoide di rotazione.M. della S. astr 1., Tom 4, 1929. |
| . |
