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Inverse problems for central forces. (English) Zbl 0859.31006

Such inverse problems were suggested by the fact that a homogeneous sphere exerts no attraction on particles in its interior, whereas on an exterior particle the force is the same as if all the masses were concentrated at the center.
The present paper refers to Newton’s Principia and to the work of Priestley, Cavendish, Bertrand, Laplace, Maxwell and further authors. It presents and discusses old and new, positive and negative results and conjectures on inverse problems; especially on the characterization of spherical surfaces by the zero resultant of inverse square forces on interior particles; or characterizations of inverse square forces by the properties of spherical surfaces or balls.
Reviewer: J.Hersch (Zürich)

MSC:

31B20 Boundary value and inverse problems for harmonic functions in higher dimensions
70-02 Research exposition (monographs, survey articles) pertaining to mechanics of particles and systems
31-02 Research exposition (monographs, survey articles) pertaining to potential theory
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